Methods and systems for characterization of an x-ray beam with high spatial resolution

ABSTRACT

Methods and systems for positioning a specimen and characterizing an x-ray beam incident onto the specimen in a Transmission, Small-Angle X-ray Scatterometry (T-SAXS) metrology system are described herein. A specimen positioning system locates a wafer vertically and actively positions the wafer in six degrees of freedom with respect to the x-ray illumination beam without attenuating the transmitted radiation. In some embodiments, a cylindrically shaped occlusion element is scanned across the illumination beam while the detected intensity of the transmitted flux is measured to precisely locate the beam center. In some other embodiments, a periodic calibration target is employed to precisely locate the beam center. The periodic calibration target includes one or more spatially defined zones having different periodic structures that diffract X-ray illumination light into distinct, measurable diffraction patterns.

CROSS REFERENCE TO RELATED APPLICATION

The present application for patent claims priority under 35 U.S.C. § 119from U.S. provisional patent application Ser. No. 62/505,014, filed May11, 2017, the subject matter of which is incorporated herein byreference in its entirety.

TECHNICAL FIELD

The described embodiments relate to x-ray metrology systems and methods,and more particularly to methods and systems for improved measurementaccuracy.

BACKGROUND INFORMATION

Semiconductor devices such as logic and memory devices are typicallyfabricated by a sequence of processing steps applied to a specimen. Thevarious features and multiple structural levels of the semiconductordevices are formed by these processing steps. For example, lithographyamong others is one semiconductor fabrication process that involvesgenerating a pattern on a semiconductor wafer. Additional examples ofsemiconductor fabrication processes include, but are not limited to,chemical-mechanical polishing, etch, deposition, and ion implantation.Multiple semiconductor devices may be fabricated on a singlesemiconductor wafer and then separated into individual semiconductordevices.

Metrology processes are used at various steps during a semiconductormanufacturing process to detect defects on wafers to promote higheryield. A number of metrology based techniques including scatterometryand reflectometry implementations and associated analysis algorithms arecommonly used to characterize critical dimensions, film thicknesses,composition and other parameters of nanoscale structures.

Traditionally, scatterometry critical dimension measurements areperformed on targets consisting of thin films and/or repeated periodicstructures. During device fabrication, these films and periodicstructures typically represent the actual device geometry and materialstructure or an intermediate design. As devices (e.g., logic and memorydevices) move toward smaller nanometer-scale dimensions,characterization becomes more difficult. Devices incorporating complexthree-dimensional geometry and materials with diverse physicalproperties contribute to characterization difficulty. For example,modern memory structures are often high-aspect ratio, three-dimensionalstructures that make it difficult for optical radiation to penetrate tothe bottom layers. Optical metrology tools utilizing infrared to visiblelight can penetrate many layers of translucent materials, but longerwavelengths that provide good depth of penetration do not providesufficient sensitivity to small anomalies. In addition, the increasingnumber of parameters required to characterize complex structures (e.g.,FinFETs), leads to increasing parameter correlation. As a result, theparameters characterizing the target often cannot be reliably decoupledwith available measurements.

In one example, longer wavelengths (e.g. near infrared) have beenemployed in an attempt to overcome penetration issues for 3D FLASHdevices that utilize polysilicon as one of the alternating materials inthe stack. However, the mirror like structure of 3D FLASH intrinsicallycauses decreasing light intensity as the illumination propagates deeperinto the film stack. This causes sensitivity loss and correlation issuesat depth. In this scenario, SCD is only able to successfully extract areduced set of metrology dimensions with high sensitivity and lowcorrelation.

In another example, opaque, high-k materials are increasingly employedin modern semiconductor structures. Optical radiation is often unable topenetrate layers constructed of these materials. As a result,measurements with thin-film scatterometry tools such as ellipsometers orreflectometers are becoming increasingly challenging.

In response to these challenges, more complex optical metrology toolshave been developed. For example, tools with multiple angles ofillumination, shorter illumination wavelengths, broader ranges ofillumination wavelengths, and more complete information acquisition fromreflected signals (e.g., measuring multiple Mueller matrix elements inaddition to the more conventional reflectivity or ellipsometric signals)have been developed. However, these approaches have not reliablyovercome fundamental challenges associated with measurement of manyadvanced targets (e.g., complex 3D structures, structures smaller than10 nm, structures employing opaque materials) and measurementapplications (e.g., line edge roughness and line width roughnessmeasurements).

Atomic force microscopes (AFM) and scanning-tunneling microscopes (STM)are able to achieve atomic resolution, but they can only probe thesurface of the specimen. In addition, AFM and STM microscopes requirelong scanning times. Scanning electron microscopes (SEM) achieveintermediate resolution levels, but are unable to penetrate structuresto sufficient depth. Thus, high-aspect ratio holes are not characterizedwell. In addition, the required charging of the specimen has an adverseeffect on imaging performance. X-ray reflectometers also suffer frompenetration issues that limit their effectiveness when measuring highaspect ratio structures.

To overcome penetration depth issues, traditional imaging techniquessuch as TEM, SEM etc., are employed with destructive sample preparationtechniques such as focused ion beam (FIB) machining, ion milling,blanket or selective etching, etc. For example, transmission electronmicroscopes (TEM) achieve high resolution levels and are able to probearbitrary depths, but TEM requires destructive sectioning of thespecimen. Several iterations of material removal and measurementgenerally provide the information required to measure the criticalmetrology parameters throughout a three dimensional structure. But,these techniques require sample destruction and lengthy process times.The complexity and time to complete these types of measurementsintroduces large inaccuracies due to drift of etching and metrologysteps. In addition, these techniques require numerous iterations whichintroduce registration errors.

Transmission, Small-Angle X-Ray Scatterometry (T-SAXS) systems employingphoton at a hard X-ray energy level (>15 keV) have shown promise toaddress challenging measurement applications. Various aspects of theapplication of SAXS technology to the measurement of critical dimensions(CD-SAXS) and overlay (OVL-SAXS) are described in 1) U.S. Pat. No.7,929,667 to Zhuang and Fielden, entitled “High-brightness X-raymetrology,” 2) U.S. Patent Publication No. 2014/0019097 by Bakeman,Shchegrov, Zhao, and Tan, entitled “Model Building And Analysis EngineFor Combined X-Ray And Optical Metrology,” 3) U.S. Patent PublicationNo. 2015/0117610 by Veldman, Bakeman, Shchegrov, and Mieher, entitled“Methods and Apparatus For Measuring Semiconductor Device Overlay UsingX-Ray Metrology,” 4) U.S. Patent Publication No. 2016/0202193 by Hench,Shchegrov, and Bakeman, entitled “Measurement System Optimization ForX-Ray Based Metrology,” 5) U.S. Patent Publication No. 2017/0167862 byDziura, Gellineau, and Shchegrov, entitled “X-ray Metrology For HighAspect Ratio Structures,” and 6) U.S. Patent Publication No.2018/0106735 by Gellineau, Dziura, Hench, Veldman, and Zalubovsky,entitled “Full Beam Metrology for X-Ray Scatterometry Systems.” Theaforementioned patent documents are assigned to KLA-Tencor Corporation,Milpitas, Calif. (USA).

SAXS has also been applied to the characterization of materials andother non-semiconductor related applications. Exemplary systems havebeen commercialized by several companies, including Xenocs SAS(www.xenocs.com), Bruker Corporation (www.bruker.com), and RigakuCorporation (www.rigaku.com/en).

Research on CD-SAXS metrology of semiconductor structures is alsodescribed in scientific literature. Most research groups have employedhigh-brightness X-ray synchrotron sources which are not suitable for usein a semiconductor fabrication facility due to their immense size, cost,etc. One example of such a system is described in the article entitled“Intercomparison between optical and x-ray scatterometry measurements ofFinFET structures” by Lemaillet, Germer, Kline et al., Proc. SPIE, v.8681, p. 86810Q (2013). More recently, a group at the National Instituteof Standards and Technology (NIST) has initiated research employingcompact and bright X-ray sources similar those described in U.S. Pat.No. 7,929,667. This research is described in an article entitled “X-rayscattering critical dimensional metrology using a compact x-ray sourcefor next generation semiconductor devices,” J. Micro/Nanolith. MEMSMOEMS 16(1), 014001 (January-March 2017).

The interaction of the X-ray beam with the target must be calibrated andaligned with the metrology system to ensure effective measurements.Exemplary characterizations include precisely locating the peakintensity of the X-ray beam on the target, measuring the X-Ray beamintensity distribution, identifying the boundaries of the X-ray beamsuch that only a certain percentage of beam flux lies outside of theboundaries. Exemplary alignments include alignment of the X-ray beamwith an optical vision system, alignment of the X-ray beam with specificmechanical features of the tool (e.g., axes of wafer rotation, etc.),etc.

In general, a wafer is navigated in the path of the X-Ray beam based onoptical measurements of alignment markers disposed throughout the waferby an optical microscope. To ensure that a particular target isprecisely navigated with respect to the X-ray beam, the beam profileneeds to be measured in the coordinates of the optical microscopeemployed to measure the markers.

In some examples, the optical microscope is aligned with a knife edgeand the knife edge is aligned with the X-ray beam. Characterization ofan X-ray beam with traditional knife edges is complicated due to thesemi-transparency of the knife material illuminated by X-ray radiationnear the edges of the knife edge. For example, tungsten has a beamattenuation length of about 8.4 micrometers when illuminated by photonshaving an energy level of 20 keV. At this length, the transmission dropsby factor of ˜1/e (e=2.718). For a knife edge shaped at an angle of 30degrees, the length of the wedge corresponding to a height of 8.4micrometer is approximately 14.5 micrometers. This simple estimate ofthe uncertainty of a knife edge position during an X-ray beam scanillustrates that when the required alignment accuracy is less than a fewmicrometers (e.g., less than 10 micrometers), the semi-transparency ofthe knife edge is limiting.

In some other examples, the X-ray beam profile is characterized by ahigh resolution X-ray camera located at some point (e.g., a focal spotof the focusing optics) with respect to the X-ray beam. In theseexamples, the beam profile is measured with the high resolution X-raycamera, and the measured coordinates of the beam are transferred to theoptical microscope employed to navigate the wafer in the path of theX-ray beam. Unfortunately, errors associated with transferring themeasured coordinates from the X-ray camera to the optical microscope aresignificant and exceed the required accuracy of navigation.

Furthermore, characterization of the X-ray beam by an X-ray camera orknife edges are intrinsically indirect and do not provide quantitativedata on photon flux incident on the target as well as photoncontamination of neighboring regions.

Future metrology applications present challenges for metrology due toincreasingly small resolution requirements, multi-parameter correlation,increasingly complex geometric structures including high aspect ratiostructures, and increasing use of opaque materials. Existing methods ofX-ray tool alignment and target navigation are limited to an accuracy ofapproximately 10-20 micrometers. These methods are not able to positionand measure metrology targets of small sizes (˜50 micrometers) in anX-ray beam with sufficient accuracy for semiconductor metrologyapplications. Thus, methods and systems for improved alignment andcalibration of X-ray beams in SAXS systems are desired to meet theplacement requirements of advanced manufacturing nodes.

SUMMARY

Methods and systems for positioning a specimen and characterizing anx-ray beam incident onto the specimen in a Transmission, Small-AngleX-ray Scatterometry (T-SAXS) metrology system are described herein.Practical T-SAXS measurements in a semiconductor manufacturingenvironment require measurements over a large range of angles ofincidence and azimuth with respect to the surface of a specimen (e.g.,semiconductor wafer) with a small beam spot size (e.g., less than 50micrometers across the effective illumination spot). Accuratepositioning of the wafer and characterization of the beam size and shapeare required to achieve small measurement box size. In addition,calibrations that accurately locate the illumination beam on the desiredtarget area on the surface of a semiconductor wafer over the full rangeof incidence and azimuth angles are presented herein.

In one aspect, a metrology tool includes a specimen positioning systemconfigured to locate a wafer vertically (i.e., plane of the wafersurface approximately aligned with the gravity vector) and activelyposition the wafer in six degrees of freedom with respect to theillumination beam. The specimen positioning system supports the wafer atthe edges; allowing the illumination beam to transmit through the waferat any location within the active area of the wafer without remounting.By supporting the wafer vertically at its edges, gravity induced sag ofthe wafer is effectively mitigated.

In a further aspect, a counterweight statically balances the rotatingmass of the specimen positioning system such that the center of gravityof the rotating mass is approximately aligned with its axis of rotation.

In some embodiments, three sensors are disposed on the specimenpositioning system to measure the distance of the backside of the waferwith respect to the specimen positioning system. In this manner, waferbow is measured and compensated by movement of the wafer using atip-tilt-Z stage.

In another aspect, a SAXS metrology system employs at least one beamocclusion calibration target to locate an x-ray illumination beam withrespect to the specimen positioning system. The beam occlusioncalibration target includes at least one marker and a cylindricallyshaped occlusion element. An alignment camera is employed to locate themarker in coordinates of the specimen positioning system. The locationof the marker with respect to the cylindrically shaped occlusion elementis known apriori (e.g., with an accuracy of less than 200 nanometers).Thus, the location of the cylindrically shaped occlusion element incoordinates of the specimen positioning system is easily determined by astraightforward coordinate transformation. The cylindrically shapedocclusion element is scanned across the illumination beam while thedetected intensity of the transmitted flux is measured. The center ofthe illumination beam is precisely located with respect to thecylindrically shaped occlusion element based on the measured intensity.Since the location of the cylindrically shaped occlusion element isknown in the coordinates of the specimen positioning system, thelocation of center of the illumination beam in the coordinates of thespecimen positioning system is precisely located by simple coordinatetransformation.

In some examples, a beam occlusion calibration target is employed tocalibrate the location of incidence of the illumination beam withrespect to the specimen positioning system. In some other examples, abeam occlusion calibration target is employed to align the axis ofrotation of the stage reference frame with respect to the illuminationbeam at the point of incidence of illumination beam with a wafer.

In another aspect, a SAXS metrology system employs at least one periodiccalibration target to locate an x-ray illumination beam with respect tothe specimen positioning system. Each periodic calibration targetincludes one or more spatially defined zones having different periodicstructures that diffract X-ray illumination light into distinctdiffraction patterns measurable by a SAXS metrology system describedherein. In addition, each periodic calibration target includes one ormore markers readable by an optical microscope to locate the periodiccalibration target with respect the specimen positioning system withhigh alignment accuracy (e.g., alignment accuracy of 0.5 micrometers orless). Each spatially defined zone has spatially well-defined boundarylines. The location of the boundary lines is known relative to themarkers with high accuracy in one or more dimensions (e.g., accuracy of0.2 micrometers or less).

In another aspect, the precise alignment of the axis of rotation withthe illumination beam in the plane of the surface of the wafer isdetermined based on the interaction of the illumination beam with two ormore beam occlusion calibration targets as measured by the x-raydetector.

In another aspect, the precise alignment of the axis of rotation with amarker of a calibration target in the plane of the surface of the waferis determined based on images of the marker collected by an alignmentcamera mounted to a lateral alignment stage.

In another aspect, the shape of the surface of the wafer in theZ-direction is mapped using any of the alignment camera, an opticalproximity sensor, a capacitive proximity sensor, an interferometry basedsensor, or any other suitable proximity sensor. In some examples, thewafer surface is mapped on the front side (i.e., patterned side) of thewafer. In some other examples, the wafer surface is mapped on the backside (i.e., unpatterned side) of the wafer, provided the thickness ofthe wafer is sufficiently uniform, well modeled, or measured in-situ orapriori.

The foregoing is a summary and thus contains, by necessity,simplifications, generalizations and omissions of detail; consequently,those skilled in the art will appreciate that the summary isillustrative only and is not limiting in any way. Other aspects,inventive features, and advantages of the devices and/or processesdescribed herein will become apparent in the non-limiting detaileddescription set forth herein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrative of a metrology system 100 configured toperform calibration of various system parameters in accordance with themethods described herein.

FIG. 2 depicts an end view of beam shaping slit mechanism 120 in oneconfiguration.

FIG. 3 depicts an end view of beam shaping slit mechanism 120 in anotherconfiguration.

FIG. 4 depicts x-ray illumination beam 116 incident on wafer 101 at aparticular orientation described by angles ϕ and θ.

FIG. 5 is a diagram illustrative of a specimen positioning system 140with the wafer stage moved to a position where the illumination beam 116is incident on wafer 101.

FIG. 6 is a diagram illustrative of specimen positioning system 140 withadditional details.

FIG. 7 depicts a beam occlusion calibration target 190 in oneembodiment.

FIG. 8A depicts a top view of illumination beam 116 incident on wafer101 as depicted in FIG. 5 where the rotational axis 153 intersects theillumination beam 116 at the point of incidence of illumination beam 116with wafer 101.

FIG. 8B depicts a top view of illumination beam 116 incident on wafer101 as depicted in FIG. 5 where rotational axis 153 is misaligned withthe surface of wafer 101 in the Z-direction.

FIG. 8C depicts a top view of illumination beam 116 incident on wafer101 as depicted in FIG. 5 where rotational axis 153 is offset fromillumination beam 116 in the X-direction.

FIG. 9 is a diagram illustrative of the specimen positioning system 140with the wafer stage moved to a position where the illumination beam 116is occluded by a cylindrical pin element 151.

FIG. 10 depicts a plot 170 illustrative of measured flux as a functionof relative position of a cylindrical pin with respect to illuminationbeam 116.

FIG. 11 depicts another illustration of specimen positioning system 140including a periodic calibration target 171 is located on wafer 101.

FIG. 12 depicts an embodiment of a periodic calibration target 210.

FIG. 13 depicts an embodiment of a periodic calibration target 220.

FIG. 14 depicts an embodiment of a periodic calibration target 230.

FIG. 15 depicts an embodiment of a periodic calibration target 240.

FIG. 16 depicts an embodiment of a periodic calibration target 250.

FIG. 17 depicts an embodiment of a periodic calibration target 260.

FIG. 18 depicts an embodiment of a periodic calibration target 270.

FIGS. 19A-B depict a set of periodic calibration targets 290 and 295,each suitable for locating an illumination beam with respect to theperiodic calibration target in one direction.

FIG. 20 depicts a periodic calibration target 280 including markers 288and 289, and seven different periodic zones 281-287 arranged in ahexagonal pattern.

FIG. 21 is a diagram illustrative of elements of metrology system 100contained in vacuum environments separate from specimen 101.

FIG. 22 is a diagram illustrative of a model building and analysisengine 180 configured to resolve specimen parameter values based onT-SAXS data in accordance with the methods described herein.

FIG. 23 depicts a flowchart illustrative of an exemplary method 300 ofcalibrating an angle of incidence offset value based on T-SAXSmeasurements at multiple angles of incidence and azimuth angles asdescribed herein.

DETAILED DESCRIPTION

Reference will now be made in detail to background examples and someembodiments of the invention, examples of which are illustrated in theaccompanying drawings.

Methods and systems for positioning a specimen and characterizing anx-ray beam incident onto the specimen in a Transmission, Small-AngleX-ray Scatterometry (T-SAXS) metrology system are described herein.Practical T-SAXS measurements in a semiconductor manufacturingenvironment require measurements over a large range of angles ofincidence and azimuth with respect to the surface of a specimen (e.g.,semiconductor wafer) with a small beam spot size (e.g., less than 50micrometers across the effective illumination spot). Accuratepositioning of the wafer and characterization of the beam size and shapeare required to achieve small measurement box size. In addition,calibrations that accurately locate the illumination beam on the desiredtarget area on the surface of a semiconductor wafer over the full rangeof incidence and azimuth angles are presented herein.

A six degree of freedom specimen positioning system is presented herein.In addition, specialized calibration targets described herein enablehigh accuracy characterization of the x-ray beam profile and highaccuracy alignment of the X-ray beam with respect to the calibrationtargets. This enables precise navigation of the wafer required tomeasure small box size metrology targets (e.g., metrology targetslocated in scribe lines having dimensions of 100 micrometer or less).

FIG. 1 illustrates an embodiment of a T-SAXS metrology tool 100 formeasuring characteristics of a specimen in at least one novel aspect. Asshown in FIG. 1, the system 100 may be used to perform T-SAXSmeasurements over an inspection area 102 of a specimen 101 illuminatedby an illumination beam spot.

In the depicted embodiment, metrology tool 100 includes an x-rayillumination subsystem 125 including an x-ray illumination source 110,focusing optics 111, beam divergence control slit 112, intermediate slit113, and beam shaping slit mechanism 120. The x-ray illumination source110 is configured to generate x-ray radiation suitable for T-SAXSmeasurements. In some embodiments, the x-ray illumination source 110 isconfigured to generate wavelengths between 0.01 nanometers and 1nanometer. In general, any suitable high-brightness x-ray illuminationsource capable of generating high brightness x-rays at flux levelssufficient to enable high-throughput, inline metrology may becontemplated to supply x-ray illumination for T-SAXS measurements. Insome embodiments, an x-ray source includes a tunable monochromator thatenables the x-ray source to deliver x-ray radiation at different,selectable wavelengths.

In some embodiments, one or more x-ray sources emitting radiation withphoton energy greater than 15 keV are employed to ensure that the x-raysource supplies light at wavelengths that allow sufficient transmissionthrough the entire device as well as the wafer substrate. By way ofnon-limiting example, any of a particle accelerator source, a liquidanode source, a rotating anode source, a stationary, solid anode source,a microfocus source, a microfocus rotating anode source, a plasma basedsource, and an inverse Compton source may be employed as x-rayillumination source 110. In one example, an inverse Compton sourceavailable from Lyncean Technologies, Inc., Palo Alto, Calif. (USA) maybe contemplated. Inverse Compton sources have an additional advantage ofbeing able to produce x-rays over a range of photon energies, therebyenabling the x-ray source to deliver x-ray radiation at different,selectable wavelengths.

Exemplary x-ray sources include electron beam sources configured tobombard solid or liquid targets to stimulate x-ray radiation. Methodsand systems for generating high brightness, liquid metal x-rayillumination are described in U.S. Pat. No. 7,929,667, issued on Apr.19, 2011, to KLA-Tencor Corp., the entirety of which is incorporatedherein by reference.

X-ray illumination source 110 produces x-ray emission over a source areahaving finite lateral dimensions (i.e., non-zero dimensions orthogonalto the beam axis. Focusing optics 111 focuses source radiation onto ametrology target located on specimen 101. The finite lateral sourcedimension results in finite spot size 102 on the target defined by therays 117 coming from the edges of the source. In some embodiments,focusing optics 111 includes elliptically shaped focusing opticalelements.

A beam divergence control slit 112 is located in the beam path betweenfocusing optics 111 and beam shaping slit mechanism 120. Beam divergencecontrol slit 112 limits the divergence of the illumination provided tothe specimen under measurement. An additional intermediate slit 113 islocated in the beam path between beam divergence control slit 112 andbeam shaping slit mechanism 120. Intermediate slit 113 providesadditional beam shaping. In general, however, intermediate slit 113 isoptional.

Beam shaping slit mechanism 120 is located in the beam path immediatelybefore specimen 101. In one aspect, the slits of beam shaping slitmechanism 120 are located in close proximity to specimen 101 to minimizethe enlargement of the incident beam spot size due to beam divergencedefined by finite source size. In one example, expansion of the beamspot size due to shadow created by finite source size is approximatelyone micrometer for a 10 micrometer x-ray source size and a distance of25 millimeters between the beam shaping slits and specimen 101.

In some embodiments, beam shaping slit mechanism 120 includes multiple,independently actuated beam shaping slits. In one embodiment, beamshaping slit mechanism 120 includes four independently actuated beamshaping slits. These four beams shaping slits effectively block aportion of incoming beam 115 and generate an illumination beam 116having a box shaped illumination cross-section.

FIGS. 2 and 3 depict an end view of beam shaping slit mechanism 120depicted in FIG. 1 in two different configurations. As illustrated inFIGS. 2 and 3, the beam axis is perpendicular to the drawing page. Asdepicted in FIG. 2, incoming beam 115 has a large cross-section. In someembodiments, incoming beam 115 has a diameter of approximately onemillimeter. Furthermore, the location of incoming beam 115 within beamshaping slits 126-129 may have an uncertainty of approximately threemillimeters due to beam pointing errors. To accommodate the size of theincoming beam and the uncertainty of the beam location, each slit has alength, L, of approximately six millimeters. As depicted in FIG. 2, eachslit is moveable in a direction perpendicular to the beam axis. In theillustration of FIG. 2, slits 126-129 are located at a maximum distancefrom the beam axis (i.e., the slits are fully open and they are notrestricting the light passing through beam shaping slit mechanism 120.

FIG. 3 depicts slits 126-129 of beam shaping slit mechanism 120 inpositions that block a portion of incoming beam 115, such that outgoingbeam 116 delivered to the specimen under measurement has reduced sizeand well-defined shape. As depicted in FIG. 3, each of slits 126-129 hasmoved inward, toward the beam axis to achieve the desired output beamshape.

Slits 126-129 are constructed from materials that minimize scatteringand effectively block incident radiation. Exemplary materials includesingle crystal materials such as Germanium, Gallium Arsenide, IndiumPhosphide, etc. Typically, the slit material is cleaved along acrystallographic direction, rather than sawn, to minimize scatteringacross structural boundaries. In addition, the slit is oriented withrespect to the incoming beam such that the interaction between theincoming radiation and the internal structure of the slit materialproduces a minimum amount of scattering. The crystals are attached toeach slit holder made of high density material (e.g., tungsten) forcomplete blocking of the x-ray beam on one side of the slit. In someembodiments, each slit has a rectangular cross-section having a width isapproximately 0.5 millimeters and a height of approximately 1-2millimeters. As depicted in FIG. 2, the length, L, of a slit isapproximately 6 millimeters.

In general, x-ray optics shape and direct x-ray radiation to specimen101. In some examples, the x-ray optics include an x-ray monochromatorto monochromatize the x-ray beam that is incident on the specimen 101.In some examples, the x-ray optics collimate or focus the x-ray beamonto measurement area 102 of specimen 101 to less than 1 milliradiandivergence using multilayer x-ray optics. In these examples, themultilayer x-ray optics function as a beam monochromator, also. In someembodiments, the x-ray optics include one or more x-ray collimatingmirrors, x-ray apertures, x-ray beam stops, refractive x-ray optics,diffractive optics such as zone plates, Montel optics, specular x-rayoptics such as grazing incidence ellipsoidal mirrors, polycapillaryoptics such as hollow capillary x-ray waveguides, multilayer optics orsystems, or any combination thereof. Further details are described inU.S. Patent Publication No. 2015/0110249, the content of which isincorporated herein by reference it its entirety.

X-ray detector 119 collects x-ray radiation 114 scattered from specimen101 and generates an output signals 135 indicative of properties ofspecimen 101 that are sensitive to the incident x-ray radiation inaccordance with a T-SAXS measurement modality. In some embodiments,scattered x-rays 114 are collected by x-ray detector 119 while specimenpositioning system 140 locates and orients specimen 101 to produceangularly resolved scattered x-rays.

In some embodiments, a T-SAXS system includes one or more photoncounting detectors with high dynamic range (e.g., greater than 10⁵). Insome embodiments, a single photon counting detector detects the positionand number of detected photons.

In some embodiments, the x-ray detector resolves one or more x-rayphoton energies and produces signals for each x-ray energy componentindicative of properties of the specimen. In some embodiments, the x-raydetector 119 includes any of a CCD array, a microchannel plate, aphotodiode array, a microstrip proportional counter, a gas filledproportional counter, a scintillator, or a fluorescent material.

In this manner the X-ray photon interactions within the detector arediscriminated by energy in addition to pixel location and number ofcounts. In some embodiments, the X-ray photon interactions arediscriminated by comparing the energy of the X-ray photon interactionwith a predetermined upper threshold value and a predetermined lowerthreshold value. In one embodiment, this information is communicated tocomputing system 130 via output signals 135 for further processing andstorage.

In a further aspect, a T-SAXS system is employed to determine propertiesof a specimen (e.g., structural parameter values) based on one or morediffraction orders of scattered light. As depicted in FIG. 1, metrologytool 100 includes a computing system 130 employed to acquire signals 135generated by detector 119 and determine properties of the specimen basedat least in part on the acquired signals.

In some examples, metrology based on T-SAXS involves determining thedimensions of the sample by the inverse solution of a pre-determinedmeasurement model with the measured data. The measurement model includesa few (on the order of ten) adjustable parameters and is representativeof the geometry and optical properties of the specimen and the opticalproperties of the measurement system. The method of inverse solveincludes, but is not limited to, model based regression, tomography,machine learning, or any combination thereof. In this manner, targetprofile parameters are estimated by solving for values of aparameterized measurement model that minimize errors between themeasured scattered x-ray intensities and modeled results.

It is desirable to perform measurements at large ranges of angle ofincidence and azimuth angle to increase the precision and accuracy ofmeasured parameter values. This approach reduces correlations amongparameters by extending the number and diversity of data sets availablefor analysis to include a variety of large-angle, out of planeorientations. For example, in a normal orientation, T-SAXS is able toresolve the critical dimension of a feature, but is largely insensitiveto sidewall angle and height of a feature. However, by collectingmeasurement data over a broad range of out of plane angularorientations, the sidewall angle and height of a feature can beresolved. In other examples, measurements performed at large ranges ofangle of incidence and azimuth angle provide sufficient resolution anddepth of penetration to characterize high aspect ratio structuresthrough their entire depth.

Measurements of the intensity of diffracted radiation as a function ofx-ray incidence angle relative to the wafer surface normal arecollected. Information contained in the multiple diffraction orders istypically unique between each model parameter under consideration. Thus,x-ray scattering yields estimation results for values of parameters ofinterest with small errors and reduced parameter correlation.

Each orientation of the illuminating x-ray beam 116 relative to thesurface normal of a semiconductor wafer 101 is described by any twoangular rotations of wafer 101 with respect to the x-ray illuminationbeam 115, or vice-versa. In one example, the orientation can bedescribed with respect to a coordinate system fixed to the wafer. FIG. 4depicts x-ray illumination beam 116 incident on wafer 101 at aparticular orientation described by an angle of incidence, θ, and anazimuth angle, ϕ. Coordinate frame XYZ is fixed to the metrology system(e.g., illumination beam 116) and coordinate frame X′Y′Z′ is fixed towafer 101. The Y axis is aligned in plane with the surface of wafer 101.X and Z are not aligned with the surface of wafer 101. Z′ is alignedwith an axis normal to the surface of wafer 101, and X′ and Y′ are in aplane aligned with the surface of wafer 101. As depicted in FIG. 4,x-ray illumination beam 116 is aligned with the Z-axis and thus lieswithin the XZ plane. Angle of incidence, θ, describes the orientation ofthe x-ray illumination beam 116 with respect to the surface normal ofthe wafer in the XZ plane. Furthermore, azimuth angle, ϕ, describes theorientation of the XZ plane with respect to the X′Z′ plane. Together, θand ϕ, uniquely define the orientation of the x-ray illumination beam116 with respect to the surface of wafer 101. In this example, theorientation of the x-ray illumination beam with respect to the surfaceof wafer 101 is described by a rotation about an axis normal to thesurface of wafer 101 (i.e., Z′ axis) and a rotation about an axisaligned with the surface of wafer 101 (i.e., Y axis). In some otherexamples, the orientation of the x-ray illumination beam with respect tothe surface of wafer 101 is described by a rotation about a first axisaligned with the surface of wafer 101 and another axis aligned with thesurface of wafer 101 and perpendicular to the first axis.

In one aspect, metrology tool 100 includes a specimen positioning system140 configured to locate a wafer vertically (i.e., plane of the wafersurface approximately aligned with the gravity vector) and activelyposition specimen 101 in six degrees of freedom with respect toillumination beam 116. In addition, specimen positioning system 101 isconfigured to align specimen 101 and orient specimen 101 over a largerange of angles of incidence (e.g., at least 70 degrees) and azimuthangle (e.g., at least 190 degrees) with respect the illumination beam116. In some embodiments, specimen positioning system 140 is configuredto rotate specimen 101 over a large range of angles of rotation (e.g.,at least 70 degrees) aligned in-plane with the surface of specimen 101.In this manner, angle resolved measurements of specimen 101 arecollected by metrology system 100 over any number of locations andorientations on the surface of specimen 101. In one example, computingsystem 130 communicates command signals (not shown) to specimenpositioning system 140 that indicate the desired position of specimen101. In response, specimen positioning system 140 generates commandsignals to the various actuators of specimen positioning system 140 toachieve the desired positioning of specimen 101.

FIG. 5 depicts a specimen positioning system 140 in one embodiment. Inone aspect, specimen positioning system 140 provides active control ofthe position of wafer 101 with respect to illumination beam 116 in allsix degrees of freedom while supporting wafer 101 vertically withrespect to the gravity vector (i.e., the gravity vector is approximatelyin-plane with the wafer surface). Specimen positioning system 140supports wafer 101 at the edges of wafer 101 allowing illumination beam116 to transmit through wafer 101 over any portion of the active area ofwafer 101 without remounting wafer 101. By supporting wafer 101vertically at its edges, gravity induced sag of wafer 101 is effectivelymitigated.

As depicted in FIG. 5, specimen positioning system 140 includes a baseframe 141, a lateral alignment stage 142, a stage reference frame 143,and a wafer stage 144 mounted to stage reference frame 143. Forreference purposes, the {X_(BF), Y_(BF), Z_(BF)} coordinate frame isattached to base frame 141, the {X_(NF), Y_(NF), Z_(NF)} coordinateframe is attached to lateral alignment stage 142, the {X_(RF), Y_(RF),Z_(RF)} coordinate frame is attached to stage reference frame 143, andthe {X_(SF), Y_(SF), Z_(SF)} coordinate frame is attached to wafer stage144. Wafer 101 is supported on wafer stage 144 by a tip-tilt-Z stage 156including actuators 150A-C. A rotary stage 158 mounted to tip-tilt-Zstage 156 orients wafer 101 over a range of azimuth angles, ϕ, withrespect to illumination beam 116. In the depicted embodiment, threelinear actuators 150A-C are mounted to the wafer stage 144 and supportrotary stage 158, which, in turn, supports wafer 101.

Actuator 145 translates the lateral alignment stage 142 with respect tothe base frame 141 along the X_(BF) axis. Rotary actuator 146 rotatesthe stage reference frame 143 with respect to lateral alignment stage142 about an axis of rotation 153 aligned with the Y_(NF) axis. Rotaryactuator 146 orients wafer 101 over a range of angles of incidence, θ,with respect to illumination beam 116. Wafer stage actuators 147 and 148translate the wafer stage 144 with respect to the stage reference frame143 along the X_(RF) and Y_(RF) axes, respectively.

In one aspect, wafer stage 144 is an open aperture, two-axis (XY) linearstacked stage. The open aperture allows the measurement beam to transmitthrough any portion of the entire wafer (e.g., 300 millimeter wafer).The wafer stage 144 is arranged such that the Y-axis stage extends in adirection approximately parallel to the axis of rotation 153.Furthermore, the Y-axis stage extends in a direction that isapproximately aligned with the gravity vector.

Actuators 150A-C operate in coordination to translate the rotary stage158 and wafer 101 with respect to the wafer stage 144 in the Z_(SF)direction and tip and tilt rotary stage 158 and wafer 101 with respectto the wafer stage 144 about axes coplanar with the X_(SF)−Y_(SF) plane.Rotary stage 158 rotates wafer 101 about an axis normal to the surfaceof wafer 101. In a further aspect, a frame of rotary stage 158 iscoupled to actuators 150A-C by a kinematic mounting system includingkinematic mounting elements 157A-C, respectively. In one example, eachkinematic mounting element 157A-C includes a sphere attached to acorresponding actuator and a V-shaped slot attached to rotary stage 158.Each sphere makes a two point contact with a corresponding V-shapedslot. Each kinematic mounting element constrains the motion of rotarystage 158 with respect to actuators 150A-C in two degrees of freedom andcollectively, the three kinematic mounting elements 157A-C constrain themotion of rotary stage 158 with respect to actuators 150A-C in sixdegrees of freedom. Each kinematic coupling element is preloaded toensure that the sphere remains in contact with the correspondingV-shaped slot at all times. In some embodiments, the preload is providedby gravity, a mechanical spring mechanism, or a combination thereof.

In another further aspect, rotary stage 158 is an open aperture, rotarystage. The open aperture allows the measurement beam to transmit throughany portion of the entire wafer (e.g., 300 millimeter wafer). The rotarystage 158 is arranged such that its axis of rotation is approximatelyperpendicular to the axis of rotation 153. Furthermore, the axis ofrotation of the rotary stage 158 is approximately perpendicular to thegravity vector. The wafer 101 is secured to the rotary stage 158 viaedge grippers to provide full wafer coverage with minimal edgeexclusion.

In summary, specimen positioning system 140 is capable of activelycontrolling the position of wafer 101 in six degrees of freedom withrespect to the illumination beam 116 such that illumination beam 116 maybe incident at any location on the surface of wafer 101 (i.e., at least300 millimeter range in X_(RF) and Y_(RF) directions). Rotary actuator146 is capable of rotating the stage reference frame 143 with respect tothe illumination beam 116 such that illumination beam 116 may beincident at the surface of wafer 101 at any of a large range of anglesof incidence (e.g., greater than two degrees). In one embodiment, rotaryactuator 146 is configured to rotate stage reference frame 143 over arange of at least sixty degrees. Rotary actuator 158 mounted to waferstage 144 is capable of rotating the wafer 101 with respect to theillumination beam 116 such that illumination beam 116 may be incident atthe surface of wafer 101 at any of a large range of azimuth angles(e.g., at least ninety degrees rotational range). In some embodiments,the range of azimuth angles is at least one hundred ninety degreesrotational range.

In some other embodiments, lateral alignment stage 142 is removed andstage reference frame 143 is rotated with respect to base frame 141 byrotary actuator 146. In these embodiments, the x-ray illumination systemincludes one or more actuators that move one or more optical elements ofthe x-ray illumination system that cause the x-ray illumination beam 116to move with respect to the base frame 141, for example, in the X_(BF)direction. In these embodiments, movements of stage reference stage 143for purposes of calibration as described herein are replaced bymovements of one or more optical elements of the x-ray illuminationsystem move the x-ray illumination beam to the desired position withrespect to the axis of rotation 153, for example. In the embodimentsdepicted in FIG. 1 and FIG. 21, computing system 130 communicatescommand signals 138 to actuator subsystem 111′ to redirect the x-rayemission relative to base frame 141 to achieve a desired beam directionby moving one or more elements of x-ray illumination subsystem 125. Inthe depicted embodiment, actuator subsystem 111′ moves focusing optics111 to redirect the x-ray emission relative to base frame 141, and thusrelocate the x-ray emission relative to the axis of rotation 153.

FIG. 6 depicts another illustration of specimen positioning system 140in greater detail. Like numbered elements depicted in FIG. 6 areanalogous to those described with reference to FIG. 5. As depicted inFIG. 5, rotary actuator 146 rotates a large mass including stagereference frame 143, wafer stage 144, tip-tilt-Z stage 156, and rotarystage 158 about the axis of rotation 153. As depicted in FIG. 6, waferstage 144, tip-tilt-Z stage 156, and rotary stage 158 is offset from theaxis of rotation 153 by a significant distance.

In a further aspect, counterweight 159 is mounted to stage referenceframe 143 to counterbalance wafer stage 144, tip-tilt-Z stage 156, androtary stage 158, etc., such that the center of gravity of the rotatingmass of the stage reference frame 143 and all mounted components isapproximately aligned with the axis of rotation 153. In this manner,force exerted by actuator 146 generates a torque about the axis ofrotation 153 with a minimum of parasitic linear forces.

As depicted in FIG. 6, air bearings 172 are employed to guide themovement of lateral alignment stage 142 with respect to base frame 141.Similarly, air bearings 171 are employed to guide the movement of stagereference frame 143 with respect to lateral alignment stage 142. Airbearings operating on precision granite surfaces minimize staticfriction and provide axis stability. This improves positioningperformance (i.e., high repeatability and small settling times) whilesupporting large loads.

To insure that the location of intersection of the illumination beam 116with the surface of wafer 101 does not change over a large range ofangles of incidence, axis of rotation 153 must have very smallsynchronous and asynchronous errors. In addition, any Abbe errors mustbe minimized. To minimize Abbe errors, air bearings 171 are equallyspaced radially about the axis of rotation 153. The bearing circle islarge enough to prevent large angular errors. The bearings areconstrained vertically by the surface of lateral alignment stage 142. Insome embodiments, the surface of lateral alignment stage 142 is aprecision ground granite surface that is perpendicular to the axis ofrotation 153.

In general, the specimen positioning system provides automatedpositioning of semiconductor wafers in six degrees of freedom. Inaddition, the specimen positioning system includes edge grippingfeatures and actuators on the rotary stage to effectively load andunload the wafer in the vertical position in coordination with a waferhandling robot.

In some embodiments, three sensors are disposed on the specimenpositioning system to measure the distance of the backside of the waferwith respect to the specimen positioning system. In this manner, thewafer bow is measured and compensated by movement of the wafer using thetip-tilt-Z stage.

In another aspect, a SAXS metrology system employs at least one beamocclusion calibration target to locate an x-ray illumination beam withrespect to the specimen positioning system. The beam occlusioncalibration target includes at least one marker and a cylindricallyshaped occlusion element. An alignment camera is employed to locate themarker in coordinates of the specimen positioning system. The locationof the marker with respect to the cylindrically shaped occlusion elementis known apriori (e.g., with an accuracy of less than 200 nanometers).Thus, the location of the cylindrically shaped occlusion element incoordinates of the specimen positioning system is easily determined by astraightforward coordinate transformation. The cylindrically shapedocclusion element is scanned across the illumination beam while thedetected intensity of the transmitted flux is measured. The center ofthe illumination beam is precisely located with respect to thecylindrically shaped occlusion element based on the measured intensity.Since the location of the cylindrically shaped occlusion element isknown in the coordinates of the specimen positioning system, thelocation of center of the illumination beam in the coordinates of thespecimen positioning system is precisely located by simple coordinatetransformation.

In some examples, a beam occlusion calibration target is employed tocalibrate the location of incidence of the illumination beam withrespect to the specimen positioning system. In some other examples, abeam occlusion calibration target is employed to align the axis ofrotation of the stage reference frame with respect to the illuminationbeam at the point of incidence of illumination beam with a wafer.

FIG. 7 depicts a beam occlusion calibration target 190 in oneembodiment. In the embodiment depicted in FIG. 7, beam occlusioncalibration target 190 includes a precision shaped cylindrical pin 192and a frame 191 that supports cylindrical pin 192. Cylindrical pin 192is fabricated with high surface quality and precise dimensions on theorder of target uncertainty (e.g., tolerances less than 0.5micrometers).

In some embodiments, frame 191 may be a structure that is mounted to aspecimen positioning system such as specimen positioning system 140. Inthese embodiments, beam occlusion calibration target 190 is mounted tospecimen positioning system 140, rather than a calibration wafer. Insome other embodiments, frame 191 may be a specialized calibration waferthat includes one or more cylindrical pins attached to the wafer itself.In these embodiments, beam occlusion calibration target 190 is mountedto a calibration wafer. Beam occlusion calibration target 190 alsoincludes openings 193 on one or both sides of cylindrical pin 192. Theopenings 193 are sized such that the illumination beam (e.g.,illumination beam 197) is able to pass through beam occlusioncalibration target 190 without occlusion (e.g., at least 2 millimetersby 2 millimeters). Beam occlusion calibration target 190 also includesone or more markers (e.g., markers 195 and 196) readable by an opticalmicroscope mounted to the specimen positioning system. The location ofmarkers 195 and 196 with respect to the edges 198 and 199 of cylindricalpin are known precisely. In this manner, the location of the edges ofcylindrical pin 192 are determined by simple coordinate transformationfrom the location of either marker 195 and 196, or both.

A cylindrical pin shaped occlusion element largely eliminates theproblem of finite transparency that arises when employing a knife edgeas an alignment target. The beam path through cylindrical pin is definedby the radius of the cylinder, R, and depth of impingement of the beampath relative to the edge of the cylindrical pin, S. When R issignificantly larger than S, the length of the beam path, L, through thecylindrical pin is approximated by equation (1).L=2√{square root over (2RS)}  (1)

When employing a tungsten carbide cylindrical pin of approximately 2millimeters diameter, the uncertainty in edge position for hard X-raysdue to semi-transparency is less than one micrometer. In general,cylindrical pin 192 may be manufactured from any suitably dense, highatomic number material. By way of non-limiting example, cylindrical pin192 may be constructed from tungsten carbide, tungsten, platinum, etc.The diameter of the cylindrical pin should be sufficiently large suchthat the induced uncertainty of the edge position due tosemi-transparency of the material is well within the total alignmenterror budget. Typically, a diameter of 2-3 millimeters is sufficient tomaintain the induced uncertainty of the edge position due tosemi-transparency of the material below one to two micrometers.

As depicted in FIG. 7, beam occlusion calibration target 190 includesone or more flat surfaces (e.g., flat surface 194) that are accuratelyaligned with the axis of cylindrical pin 192. In some examples, thesurface 194 is a reference surface for measurement of the targetposition in the direction collinear with the X-ray beam axis by adistance sensor (e.g., capacitive probe, inductive probe, etc.). Inaddition, in some embodiments, one or more markers are located on theflat surface. For example, as depicted in FIG. 7, marker 195 is locatedon the flat surface 194.

In the embodiment depicted in FIG. 5, beam occlusion calibration targets151 and 152 are mounted to the frame of rotary stage 158 such that thecentral axis of the cylindrical pins are approximately co-planar withthe surface of wafer 101. As depicted in FIG. 5, cylindrical pin 151includes a central axis approximately aligned parallel with the Y_(NF)axis and cylindrical pin 152 includes a central axis approximatelyaligned parallel with the X_(RF) axis. Each cylindrical pin occludes thebeam by absorption of a large fraction of any impinging x-rays.

Specimen positioning system 140 also includes an alignment camera 154mounted to stage reference frame 143. In the depicted embodiment, thealignment camera is mounted to the stage reference frame, and thusrotates with the stage reference frame. Alignment camera 154 isconfigured to generate high resolution images of objects in its field ofview, such as wafer 101. In some embodiments, alignment camera 154 alsoincludes an auto-focus mechanism that maintains a sharp image focus byprecisely moving the focal point of the camera by a measured distance.In some of these embodiments, alignment camera 154 can be used tomeasure relative distances between the stage reference frame to whichthe camera body is mounted and wafer 101 or markers 151A and 152A imagedby the camera by monitoring the z-displacement of the focal point of thecamera.

In some other embodiments, an alignment camera is mounted to lateralalignment stage 142. In some of these embodiments, the alignment camerais used to measure relative distances between the {X_(NF), Y_(NF),Z_(NF)} coordinate frame to which the camera body is mounted and wafer101 or markers 151A and 152A imaged by the camera by monitoring thelocation of optical markers mounted to wafer 101 or markers 151A and152A within the field of view of the alignment camera.

In one further aspect, the precise location of incidence of theillumination beam in two dimensions in the plane of the surface of thewafer is determined based on the interaction of the illumination beamwith two or more beam occlusion calibration targets.

FIG. 9 is a diagram illustrative of the specimen positioning system 140with the wafer stage moved to a position where the illumination beam 116is occluded by the cylindrical pin element 151. The precise location ofincidence of the illumination beam with respect to cylindrical pin 151is determined based on transmitted flux measured by detector 119 as afunction of the X position of cylindrical pin 151 with respect toillumination beam 116 (i.e., base frame 141). As depicted in FIG. 9, ascylindrical pin 151 is moved in the positive X-direction (in thedirection of X_(BF)), more and more of illumination beam 116 is occludedby cylindrical pin 151. As a result fewer photons reach detector 119.However, as cylindrical pin 151 is moved in the negative X-direction(opposite X_(BF)), less and less of illumination beam 116 is occluded bycylindrical pin 151. Detector 119 generates signals 155 indicative ofthe measured flux as a function of X-position and the results areanalyzed to identify the position of the cylindrical pin thatcorresponds with the center of illumination beam 116.

FIG. 10 depicts a plot 170 illustrative of measured flux as a functionof relative position of a cylindrical pin with respect to illuminationbeam 116. The depicted relationship between measured flux 155 andrelative position is a sigmoid type function (e.g., logistic or othererror function depending on the beam profile).

In some examples, the beam center is determined to be the relativeposition of the cylindrical pin with respect to the illumination beamwhere the measured flux is halfway between the minimum flux value,F_(MIN), and the maximum flux value, F_(MAX), or the maximum value ofthe derivative, dF/dx. However, in some other examples, the beam centermay be determined at another flux value different from the middle of therange of measured flux. In some examples, a more precise relationship isdetermined by modeling of the interaction of the beam with the materialand geometry of the cylindrical pin. In these examples, the modelledinteraction is compared with the measured transmitted flux, and afitting algorithm is used to determine the relative position of thecylindrical pin with respect to the illumination beam that aligns withthe beam center based on the fit of the measured results to the model.

In one example, an estimate of the distance, AX, between a currentposition of cylindrical pin 151 with respect to the center ofillumination beam 116 and a position of the cylindrical pin 151 thatcoincides with the beam center is based on the measured flux, F_(MEAS),the mid-point of the flux, F_(MID), and the inverse of the derivative ofthe measured flux as a function of cylindrical pin position as describedby equation (2)

$\begin{matrix}{{\Delta\; X} = {\frac{\partial X}{\partial F}\left( {F_{MEAS} - F_{MID}} \right)}} & (2)\end{matrix}$and F_(MID) is described by equation (3).

$\begin{matrix}{F_{MID} = \frac{F_{MIN} + F_{MAX}}{2}} & (3)\end{matrix}$

The maximum and minimum values of measured flux can be measured byscanning the wafer stage while measuring transmitted flux. Furthermore,the slope at the mid-point can also be estimated. Based on thesequantities, an estimate of the change in centered position of thecylindrical pin is determined in accordance with equation (2) simply bymeasuring flux at one position. If necessary, the change in centeredposition can be determined iteratively to converge on a centeredposition.

Since the beam has a centroid component in two directions (e.g., X and Ydirections), two cylindrical pins each oriented perpendicular to thedirection of the centroid component are measured. In the embodimentdepicted in FIG. 9, cylindrical pin 151 is employed to locate the beamcenter with respect to the stage reference frame in the X-direction andcylindrical pin 152 is employed to locate the beam center with respectto the stage reference frame in the Y-direction. In general, more thantwo cylindrical pins may be utilized to generate redundancy and increasethe accuracy of the calibration of the beam location.

As depicted in FIG. 9, the center of the illumination beam 116 isaligned with the edges of the vertically and horizontally orientedcylindrical pins 151 and 152 as described hereinbefore. In theembodiment depicted in FIG. 9, a fiducial mark 151A is located co-planarwith the central axis of cylindrical pin 151. Similarly, a fiducial mark152A is located co-planar with the central axis of cylindrical pin 152.At the location of beam center alignment with cylindrical pin 151, theposition of the illumination beam 116 with respect to cylindrical pin151, or fiducial 151A at or near the cylindrical pin, is recorded byalignment camera 154. This registers the relative position of theillumination beam with respect to a precise location in the field ofview of the alignment camera (assuming no change in focus position). Asdepicted in FIG. 5, wafer 101 is moved within the field of view ofalignment camera 154. Wafer 101 is moved such that a desired location(e.g., a fiducial mark) on the wafer is imaged within the field of viewof alignment camera 154. The position of the illumination beam 116 withrespect to the desired location is determined by alignment camera 154based on the previous registration. In this manner, the position of theillumination beam 116 on wafer 101 in the X and Y direction is quicklyestimated based on an image collected by the alignment camera 154. Insome embodiments, the position of the wafer in the Z-direction withrespect to the Z-location of cylindrical pin 151 is measured by changingthe focus position of alignment camera 154 until the lithographicfeatures on the surface of wafer 101 come into precise focus. The changeis focus position is indicative of the difference in Z-position betweenthe cylindrical pin and the imaged location on the wafer. In some otherembodiments, the position of the wafer in the Z-direction with respectto the Z-location of cylindrical pin 151 is measured by one or moreoptical proximity sensors, capacitive proximity sensors, interferometrybased sensors, or other suitable proximity sensors. Actuators 150A-C maybe employed to reposition wafer 101 in the Z-direction to relocate theimaged location to be in plane with the cylindrical pin (e.g. fiducial151A).

In a further aspect, the position of incidence of the illumination beamis determined at any location on the wafer based on wafer stagecoordinates. Once the center of the illumination beam is aligned withthe vertical and horizontal cylindrical pins, and the position of theillumination beam with respect to the cylindrical pin is recorded by analignment camera as described hereinbefore, the location of incidence ofthe illumination beam can be transferred to stage coordinates. Asdepicted in FIG. 5, wafer 101 is moved within the field of view ofalignment camera 154. The movement of wafer 101 is measured by theposition measurement system of wafer stage 144 (e.g., linear encoders,etc.) By moving wafer 101 to three or more desired locations (e.g., afiducial marks) on the wafer imaged within the field of view ofalignment camera 154, the position of the illumination beam with respectto the desired location is determined at each desired location, alongwith the position of the wafer in stage coordinates. Based on the knownlocation of the illumination beam and stage coordinates at the three ormore locations, a map is generated that relates stage coordinates to thelocation of incidence of the illumination beam.

After locating the cylindrical pin 151 at the center of illuminationbeam 116 (in the X-direction), alignment camera 154 images the locationof the cylindrical pin itself, or a fiducial mark located on or near thecylindrical pin, to establish a relationship between beam location andimage location within the field of view of alignment camera 154. Sincealignment camera 154 is located in a fixed, or repeatable, position withrespect to the stage reference frame 143, the image registers thelocation of the illumination beam with respect to the stage referenceframe 143, and thus serves as a reference for beam location in theX-direction. Moreover, alignment camera 154 establishes a precise focusposition of the fiducial mark, to establish a precise Z-location of thecylindrical pin with respect to stage reference frame 143. Forembodiments where the alignment camera 154 rotates with the stagereference frame, the focus position of the alignment camera 154 servesas a reference for Z-position of the cylindrical pin with respect to thestage reference frame.

Since occluded flux is utilized to estimate the location of beamincidence, there is a risk that changes in flux in the illumination beamwill be interpreted as a shift in position. In some embodiments, theflux of the illumination beam is measured immediately before, after, orsimultaneously with the occlusion measurements. Variations inillumination flux are compensated in analysis of the measured flux 155to eliminate their influence on the measurement.

In another aspect, the precise alignment of the axis of rotation 153with the illumination beam in the plane of the surface of the wafer isdetermined based on the interaction of the illumination beam with two ormore beam occlusion calibration targets as measured by the x-raydetector 119.

To ensure measurement integrity, the location of incidence ofillumination beam 116 on the surface of wafer 101 should remainstationary during measurements over a large range of angles of incidenceand azimuth angles. To achieve this objective, the axis of rotation 153of stage reference frame 143 must be approximately co-planar with thesurface of wafer 101 at the measurement location. Furthermore, the axisof rotation 153 must be aligned with the illumination beam 116 in theX_(BF) direction such that the axis of rotation 153 intersects theillumination beam 116 at the point of incidence of illumination beam 116with wafer 101 at the measurement location.

FIG. 8A depicts a top view of illumination beam 116 incident on wafer101 as depicted in FIG. 5. FIG. 8A depicts an end view of rotationalaxis 153 in a state of alignment where rotational axis 153 intersectsthe illumination beam 116 at the point of incidence of illumination beam116 with wafer 101 at location 103 on wafer 101. As depicted in FIG. 8A,as wafer 101 is rotated about rotational axis 153 over a large angle ofincidence, θ, illumination beam 116 remains incident at location 103.Thus, in this scenario, the location of incidence of illumination beam116 on the surface of wafer 101 remains stationary during measurementsover a large range of angles of incidence.

FIG. 8B depicts a top view of illumination beam 116 incident on wafer101 as depicted in FIG. 5. FIG. 8B depicts an end view of rotationalaxis 153 in a state of alignment where rotational axis 153 is misalignedwith the surface of wafer 101 by a distance ∂z. As depicted in FIG. 8B,as wafer 101 is rotated about rotational axis 153 over a large angle ofincidence, θ, a portion of location 103 is no longer illuminated (i.e.,some other portion of wafer 101 is illuminated instead. Thus, in thisscenario, the location of incidence of illumination beam 116 on thesurface of wafer 101 drifts during measurements over a large range ofangles of incidence, which is highly undesirable.

FIG. 8C depicts a top view of illumination beam 116 incident on wafer101 as depicted in FIG. 5. FIG. 8C depicts an end view of rotationalaxis 153 in a state of alignment where rotational axis 153 is co-planarwith the surface of wafer 101, but is offset from illumination beam 116by a distance ∂x. As depicted in FIG. 8C, as wafer 101 is rotated aboutrotational axis 153 over a large angle of incidence, θ, a portion oflocation 103 is no longer illuminated (i.e., some other portion of wafer101 is illuminated instead. Thus, in this scenario, the location ofincidence of illumination beam 116 on the surface of wafer 101 driftsduring measurements over a large range of angles of incidence, which ishighly undesirable.

In some embodiments, the calibration of the axis of rotation of thestage reference frame is achieved by aligning the center of theillumination beam with the X-direction cylindrical pin 151 and measuringflux at a plurality of different rotational positions of the stagereference frame, θ. The apparent motion of the cylindrical pin in theX-direction (ΔX) is determined based on the chosen occlusion model asdescribed hereinbefore (e.g., the sigmoid function depicted in FIG. 10,or another model). In addition, the apparent motion of the cylindricalpin in the X-direction is a function of 1) the distance of thecylindrical pin from the axis of rotation in the x-direction, ∂x, and inthe z-direction, ∂z, 2) the distance from the beam center and the axisof rotation 153 in the x-direction, ∂n, and 3) the rotation angle aboutthe axis of rotation 153 of the stage reference frame, θ. Therelationship is described in equation (4).ΔX=∂x cos θ+∂z sin θ+∂n  (4)

In one example, transmitted flux is measured at three angles ofincidence, {−Θ, 0, +Θ}. A linear system of equations described byequation (5) results from equation (4).

$\begin{matrix}{\begin{bmatrix}{\Delta\; X_{+}} \\{\Delta\; X_{0}} \\{\Delta\; X_{-}}\end{bmatrix} = {{\begin{bmatrix}1 & {\cos\;\Theta} & {\sin\;\Theta} \\1 & 1 & 0 \\1 & {\cos\;\Theta} & {{- \sin}\;\Theta}\end{bmatrix}\begin{bmatrix}{\partial n} \\{\partial x} \\{\partial z}\end{bmatrix}} = {A_{\Theta}\begin{bmatrix}{\partial n} \\{\partial x} \\{\partial z}\end{bmatrix}}}} & (5)\end{matrix}$

Equation (6) is obtained by inverting equation (5). Equation (6) solvesfor values of ∂n, ∂x, and ∂z from the apparent motion of the cylindricalpin in the X-direction.

$\begin{matrix}{\begin{bmatrix}{\partial n} \\{\partial x} \\{\partial z}\end{bmatrix} = {{{\frac{1}{2\left( {{\cos\;\Theta} - 1} \right)}\begin{bmatrix}{- 1} & {2\;\cos\;\Theta} & {- 1} \\1 & {- 2} & 1 \\\frac{\left( {{\cos\;\Theta} - 1} \right)}{\sin\;\Theta} & 0 & {- \frac{\left( {{\cos\;\Theta} - 1} \right)}{\sin\;\Theta}}\end{bmatrix}}\begin{bmatrix}{\Delta\; X_{+}} \\{\Delta\; X_{0}} \\{\Delta\; X_{-}}\end{bmatrix}} = {A_{\Theta}^{- 1}\Delta_{X}}}} & (6)\end{matrix}$

Equation (6) combined with equation (3) solves for values of ∂n, ∂x, and∂z from the apparent motion of the cylindrical pin in the X-directiondetermined from measured flux. In some examples, the solution for valuesof is ∂n, ∂x, and ∂z is obtained iteratively as described by equation(7).

$\begin{matrix}{{w_{k + 1} = {w_{k} + {\frac{\partial X}{\partial F}{A_{\Theta}^{- 1}\begin{bmatrix}{F_{+} - F_{MID}} \\{F_{0} - F_{MID}} \\{F_{-} - F_{MID}}\end{bmatrix}}}}},{where}} & (7)\end{matrix}$where k is the iteration index and w is the vector [∂n, ∂x, and ∂z] ofthe values of the displacements of the actuators of specimen positioningsystem 140 required to align the axis of rotation 153 with theknife-edge 151 in the X and Z directions. The displacement, ∂n, isrealized by actuator 145 moving the entire stage reference frame 143with respect to the illumination beam 116 in the X-direction. Thedisplacement, ∂x, is realized by actuator 147 moving the cylindrical pin151 back into alignment with the beam. The displacement, ∂z, is realizedby actuators 150A-C moving the cylindrical pin in the Z-direction toalign the axis of rotation 153 in plane with the central axis of thecylindrical pin in the Z-direction. Starting at an initial estimate, w₀,the recursion of equation (7) will converge to a point where the axis ofrotation 153 is aligned to the cylindrical pin 151.

In general, equation (7) does not need to be applied exactly. The valuesof A_(Θ) and ∂x/∂F may be approximated numerically. In other examples,other matrices may be used, provided the iteration is stable andconverges to the correct value.

In general, transmitted flux may be measured at any three or moredifferent angles of incidence to determine values of displacementsrequired to align the axis of rotation 153 with the cylindrical pin 151in the X and Z directions. The selection of any three different anglesof incidence results in a linear of system of equations that can bedirectly inverted. The selection of four of more different angles ofincidence results in an overdetermined linear system of equations thatcan be solved with a pseudoinverse algorithm to determine values ofdisplacements required to align the axis of rotation 153 with thecylindrical pin 151 in the X and Z directions. The terms of the matricesillustrated in equations (5) and (6) depend on the selected angles ofincidence. Thus, the terms will differ from equations (5) and (6) inexamples where different angles of incidence are selected.

In another aspect, the precise alignment of the axis of rotation 153with a marker of a calibration target (e.g., marker 151A of beamocclusion calibration target 151, marker located on wafer 101, etc.) inthe plane of the surface of the wafer is determined based on images ofthe marker collected by an alignment camera mounted to lateral alignmentstage 142.

The apparent motion of the marker in the X-direction (ΔX) in the fieldof view of the alignment camera is a function of the distance of themarker from the axis of rotation in the x-direction, ∂x, and in thez-direction, ∂z, and the rotation angle about the axis of rotation 153of the stage reference frame, θ. For an alignment camera mounted tolateral alignment stage 142 the relationship is described in equation(8).ΔX=∂x(1−cos θ)+∂z(sin θ)  (8)

In some examples, the X-position of a marker (e.g., marker 151A) ismeasured at any three different angles of incidence to determine valuesof displacements required to align the axis of rotation 153 with thecylindrical pin 151 in the X and Z directions. The selection of anythree different angles of incidence results in a linear of system ofequations that can be directly inverted to solve for the distance of themarker from the axis of rotation in the x-direction, ∂x, and in thez-direction, ∂z.

For an idealized beam occlusion calibration target and axis of rotation,it would be sufficient to have only one beam occlusion calibrationtarget for beam calibration. Depending on the requirements of thesystem, however, multiple beam occlusion calibration targets may berequired. By aligning edges of multiple occlusion elements, it ispossible to deduce any deviation of the axis of rotation from thenominal Y_(NF) axis. Also, multiple identical occlusion elements allowthe calibration of an edge from the right and the left, or up and down,helping eliminate systematic errors in the imaged edges (i.e., imaged byalignment camera 154) and the apparent edge deduced from the occludedflux change.

In another aspect, a SAXS metrology system employs at least one periodiccalibration target to locate an x-ray illumination beam with respect tothe specimen positioning system. Each periodic calibration targetincludes one or more spatially defined zones having different periodicstructures that diffract X-ray illumination light into distinctdiffraction patterns measurable by a SAXS metrology system describedherein. In addition, each periodic calibration target includes one ormore markers readable by an optical microscope to locate the periodiccalibration target with respect the specimen positioning system withhigh alignment accuracy (e.g., alignment accuracy of 0.5 micrometers orless). Each spatially defined zone has spatially well-defined boundarylines. The location of the boundary lines is known relative to themarkers with high accuracy in one or more dimensions (e.g., accuracy of0.2 micrometers or less).

In some embodiments, the size of each periodic zone is designed to belarger than the projection of the illumination beam onto the periodiccalibration target. In this manner, the beam profile can becharacterized by scanning the illumination beam across an interfacebetween two different periodic zones each sized larger than theillumination beam. In some embodiments, illumination beam 116 has a beamwidth of less than 200 micrometers. In some embodiments, illuminationbeam 116 has a beam width of less than 100 micrometers. In someembodiments, illumination beam 116 has a beam width of less than 50micrometers. In addition, in some examples, calibration measurements areperformed at large angles of incidence. In these examples, theprojection of illumination beam onto the periodic calibration target iselongated in one direction, and each periodic zone is sized larger thanthe projected illumination area.

In some embodiments, the dimensions of each periodic zone differdepending on direction with respect to the illumination beam. Forexample, a periodic zone may be larger in a direction perpendicular tothe axis of rotation 153 to accommodate a large angle of incidence. Inanother example, the illumination beam may be larger in one directionthan another (e.g., a rectangular illumination beam shape) and aperiodic zone may be larger in the elongated direction.

In some embodiments, the dimensions of one or more of the periodic zonesare sized to match the required measurement box size. In one example,one of the periodic zones is sized to match the illumination beam size(e.g., 50 micrometers or 100 micrometers square) or some other numberfor calibration of the alignment of the axis of rotation 153 withrespect to the illumination beam 116. In this example, perfect alignmentis achieved when the illumination beam 116 does not move relative to theperiodic calibration target over a large range of AOI. In this example,if the illumination beam moves relative to the periodic calibrationtarget as AOI changes, the illumination beam will move from the periodicsized to match the illumination beam size to an adjacent periodic zone.This movement of the illumination beam across the boundary between zonesis detected by the detector 119.

In general, a set of periodic calibration targets or set of zones of aperiodic calibration target includes different sized zones useful forcharacterizing beam profile and size. In general, one or more zones mayhave sized to be larger, smaller, or the same size as the illuminationbeam.

In general, the periodicity of a periodic calibration target isoptimized to enhance x-ray scattering contrast. The pitch of eachperiodic structure is small enough to ensure adequate spatial separationof the detected orders at the detector. The angle of each diffractedorder should be significantly larger than the beam divergence to ensureadequate spatial separation, and the angle of each diffracted orderincreases as the pitch decreases. In some embodiments, the pitch of eachperiodic structure should be one the order of 0.1 micrometer (e.g., lessthan 200 nanometers) to ensure adequate spatial separation andmeasurement accuracy.

Each periodic structure is made of a material having high contrast withhard X-rays and large atomic number (e.g., Tungsten, Tungsten Carbide,Platinum, etc.).

In addition, each periodic structure is fabricated with sufficientheight to generate a measurable diffraction pattern over a reasonableexposure time. In some examples, a periodic structure having a height of0.5 millimeter or more is advantageous.

In some embodiments, any of the periodic calibration targets describedherein is mounted to a specimen positioning system, such as specimenpositioning system 140. In some other embodiments, any of the periodiccalibration targets described herein is mounted to a calibration waferor a production wafer under measurement.

FIG. 11 depicts another illustration of specimen positioning system 140in greater detail. Like numbered elements depicted in FIG. 11 areanalogous to those described with reference to FIG. 5. In the embodimentdepicted in FIG. 11, a periodic calibration target 171 is located onwafer 101.

The periodic calibration target 171 includes at least one marker andmultiple periodic structures (e.g., gratings). If the illumination beam116 is incident on two or more different diffraction patterns, the ratioof measured intensities of the orders associated with the differentperiodic structures provides information about the location of theillumination beam with respect to the illuminated patterns. Alignmentcamera 154 is employed to locate the marker in coordinates of thespecimen positioning system. The location of the marker with respect tothe periodic structure is known apriori. Thus, the location of theperiodic structure in coordinates of the specimen positioning system iseasily determined by a straightforward coordinate transformation. Theperiodic calibration target 171 is scanned across illumination beam 116while the detected intensities of the diffracted orders are measured bydetector 119. The center of the illumination beam 116 is preciselylocated with respect to the periodic calibration target 171 based on themeasured intensities. Since the location of the periodic calibrationtarget 171 is known in the coordinates of the specimen positioningsystem, the location of center of the illumination beam in thecoordinates of the specimen positioning system is precisely located bysimple coordinate transformation.

In some examples, a periodic calibration target is employed to calibratethe location of incidence of the illumination beam with respect to thespecimen positioning system. In some other examples, a periodiccalibration target is employed to align the axis of rotation of thestage reference frame with respect to the illumination beam at the pointof incidence of the illumination beam with a wafer. In some otherexamples, a periodic calibration target is scanned across theillumination beam at many azimuth angles. In this manner, the beamprofile is characterized in addition to calibrating the position of theillumination beam with respect to the target.

In some embodiments, a periodic calibration target includes a centralperiodic zone and one or more periodic zones surrounding the centralperiodic zone. Each periodic zone includes a different pitch, adifferent pitch orientation, or a combination thereof.

FIG. 12 depicts an embodiment of a periodic calibration target 210. Asdepicted in FIG. 12 periodic calibration target 210 includes markers 211and 212 readable by an optical microscope mounted to the specimenpositioning system, a small pitch periodic structure 215 located in acentral zone 214 and a larger pitch periodic structure 213 in aperipheral zone around the central zone 214. Markers 211 and 212 arelocated in plane with the periodic structures of the periodiccalibration target. In addition, the location of markers 211 and 212with respect to the boundaries of central zone 214 are known precisely.In this manner, the location of the boundaries are determined by simplecoordinate transformation from the location of either marker 211 and212, or both.

Illumination of central zone 214 (i.e., periodic structure 215) byillumination beam 116 causes diffraction of multiple orders acrossdetector 119 in a horizontal direction with relatively large spacing(e.g., 100 micrometers). Illumination of the peripheral zone (i.e.,periodic structure 213) by illumination beam 116 causes diffraction ofmultiple orders across detector 119 in a horizontal direction with asmaller spacing due to the larger pitch of grating 213. The ratio ofintensities between the measured orders of grating 215 and grating 213indicates the location of illumination beam 116 relative to boundarylines between central zone 214 and the peripheral zone.

FIG. 13 depicts an embodiment of a periodic calibration target 220. Asdepicted in FIG. 13 periodic calibration target 220 includes markers 221and 222 readable by an optical microscope mounted to the specimenpositioning system, a vertically disposed periodic structure 225 locatedin a central zone 224 and a horizontally disposed periodic structure 223in a peripheral zone around the central zone 224. Markers 221 and 222are located in plane with the periodic structures of the periodiccalibration target. In addition, the location of markers 221 and 222with respect to the boundaries of central zone 224 are known precisely.In this manner, the location of the boundaries are determined by simplecoordinate transformation from the location of either marker 221 and222, or both.

Illumination of central zone 224 (i.e., periodic structure 225) byillumination beam 116 causes diffraction of multiple orders acrossdetector 119 in a horizontal direction. Illumination of the peripheralzone (i.e., periodic structure 223) by illumination beam 116 causesdiffraction of multiple orders across detector 119 in a verticaldirection. The ratio of intensities between the measured orders ofgrating 225 and grating 223 indicates the location of illumination beam116 relative to boundary lines between central zone 224 and theperipheral zone.

FIG. 14 depicts an embodiment of a periodic calibration target 230. Asdepicted in FIG. 14 periodic calibration target 230 includes markers 231and 232 readable by an optical microscope mounted to the specimenpositioning system, a horizontally disposed periodic structure 233 in aperipheral zone around a central zone 234 having no periodic structureat all. Markers 231 and 232 are located in plane with the periodicstructures of the periodic calibration target. In addition, the locationof markers 231 and 232 with respect to the boundaries of central zone234 are known precisely. In this manner, the location of the boundariesare determined by simple coordinate transformation from the location ofeither marker 231 and 232, or both.

Illumination of central zone 234 by illumination beam 116 causes nodiffraction; only the zero order is detected. Illumination of theperipheral zone (i.e., periodic structure 233) by illumination beam 116causes diffraction of multiple orders across detector 119 in a verticaldirection. The ratio of intensities between the measured orders ofgrating 233 and the zero order intensity indicates the location ofillumination beam 116 relative to boundary lines between central zone234 and the peripheral zone.

In some embodiments, a periodic calibration target includes any numberof periodic zones that intersect at a common point. In this manner, theX-ray illumination beam is aligned with the common point shared by eachof the periodic zones. Each periodic zone includes a different pitch, adifferent pitch orientation, or a combination thereof.

FIG. 15 depicts an embodiment of a periodic calibration target 240. Asdepicted in FIG. 15 periodic calibration target 240 includes markers 241and 242 readable by an optical microscope mounted to the specimenpositioning system and four periodic zones located in a quadraturearrangement. As depicted in FIG. 15, a vertically disposed periodicstructure 243 is located in a first quadrant, a horizontally disposedperiodic structure 244 is located in a second quadrant, a verticallydisposed periodic structure 245 is located in a third quadrant, and ahorizontally disposed periodic structure 246 is located in a fourthquadrant. Markers 241 and 242 are located in plane with the periodicstructures of the periodic calibration target. In addition, the locationof markers 241 and 242 with respect to the common point in the center ofthe quadrature arrangement is known precisely. In this manner, thelocation of the common point is determined by simple coordinatetransformation from the location of either marker 241 and 242, or both.

Illumination of structures 243 and 245 by illumination beam 116 causesdiffraction of multiple orders across detector 119 in a horizontaldirection.

Illumination of structures 244 and 246 by illumination beam 116 causesdiffraction of multiple orders across detector 119 in a verticaldirection. The ratio of intensities between the measured ordersindicates the location of illumination beam 116 relative to the commonpoint shared by structures 243-246.

FIG. 16 depicts an embodiment of a periodic calibration target 250. Asdepicted in FIG. 16 periodic calibration target 250 includes markers 251and 252 readable by an optical microscope mounted to the specimenpositioning system and four periodic zones located in a quadraturearrangement. As depicted in FIG. 16, a periodic structure 253 orientedat −45 degrees with respect to vertical is located in a first quadrant,a periodic structure 254 oriented at 45 degrees with respect to verticalis located in a second quadrant, a horizontally disposed periodicstructure 255 is located in a third quadrant, and a vertically disposedperiodic structure 256 is located in a fourth quadrant. Markers 251 and252 are located in plane with the periodic structures of the periodiccalibration target. In addition, the location of markers 251 and 252with respect to the common point in the center of the quadraturearrangement is known precisely. In this manner, the location of thecommon point is determined by simple coordinate transformation from thelocation of either marker 251 and 252, or both.

Illumination of structures 253 and 254 by illumination beam 116 causesdiffraction of multiple orders across detector 119 at +45 and −45degrees, respectively. Illumination of structures 255 and 256 byillumination beam 116 causes diffraction of multiple orders acrossdetector 119 in a vertical and horizontal direction, respectively. Theratio of intensities between the measured orders indicates the locationof illumination beam 116 relative to the common point shared bystructures 253-256.

FIG. 17 depicts an embodiment of a periodic calibration target 260. Asdepicted in FIG. 17 periodic calibration target 260 includes markers 261and 262 readable by an optical microscope mounted to the specimenpositioning system and four periodic zones located in a quadraturearrangement. As depicted in FIG. 17, a vertically disposed periodicstructure 263 having a relatively small pitch is located in a firstquadrant, a horizontally disposed periodic structure 264 having arelatively large pitch is located in a second quadrant, a verticallydisposed periodic structure 265 having a relatively large pitch islocated in a third quadrant, and a horizontally disposed periodicstructure 246 having a relatively small pitch is located in a fourthquadrant. Markers 261 and 262 are located in plane with the periodicstructures of the periodic calibration target. In addition, the locationof markers 261 and 262 with respect to the common point in the center ofthe quadrature arrangement is known precisely. In this manner, thelocation of the common point is determined by simple coordinatetransformation from the location of either marker 261 and 262, or both.

Illumination of structures 263 and 265 by illumination beam 116 causesdiffraction of multiple orders across detector 119 in a horizontaldirection. Illumination of structures 264 and 266 by illumination beam116 causes diffraction of multiple orders across detector 119 in avertical direction. The orders associated with structures 263 and 266are spaced differently than the orders associated with structures 264and 265. The ratio of intensities between the measured orders indicatesthe location of illumination beam 116 relative to the common pointshared by structures 263-266.

FIG. 18 depicts an embodiment of a periodic calibration target 270. Asdepicted in FIG. 18 periodic calibration target 270 includes markers 271and 272 readable by an optical microscope mounted to the specimenpositioning system and four periodic zones located in a quadraturearrangement. As depicted in FIG. 18, a vertically disposed periodicstructure 273 having a relatively small pitch is located in a firstquadrant, a horizontally disposed periodic structure 274 having arelatively large pitch is located in a second quadrant, a verticallydisposed periodic structure 275 having a relatively small pitch islocated in a third quadrant, and a horizontally disposed periodicstructure 276 having a relatively large pitch is located in a fourthquadrant. Markers 271 and 272 are located in plane with the periodicstructures of the periodic calibration target. In addition, the locationof markers 271 and 272 with respect to the common point in the center ofthe quadrature arrangement is known precisely. In this manner, thelocation of the common point is determined by simple coordinatetransformation from the location of either marker 271 and 272, or both.

Illumination of structures 273 and 275 by illumination beam 116 causesdiffraction of multiple orders across detector 119 in a horizontaldirection. Illumination of structures 274 and 276 by illumination beam116 causes diffraction of multiple orders across detector 119 in avertical direction. The orders associated with structures 273 and 275are spaced differently than the orders associated with structures 274and 276. The ratio of intensities between the measured orders indicatesthe location of illumination beam 116 relative to the common pointshared by structures 273-276.

FIGS. 19A-B depict a set of periodic calibration targets 290 and 295,each suitable for locating an illumination beam with respect to theperiodic calibration target in one direction. When targets 290 and 295are both employed to calibrate a SAXS metrology system, the location ofthe illumination beam relative to the specimen positioning system isdetermined in two orthogonal dimensions. As depicted in FIG. 19Aperiodic calibration target 290 includes markers 291 and 292 readable byan optical microscope mounted to the specimen positioning system and twoperiodic zones located adjacent to one another along a boundary line. Asdepicted in FIG. 19A, a horizontally disposed periodic structure 293 islocated alongside a vertically disposed periodic structure 294. Markers291 and 292 are located in plane with the periodic structures of theperiodic calibration target. In addition, the location of markers 291and 292 with respect to the boundary between structures 293 and 294 isknown precisely. In this manner, the location of the boundary line isdetermined by simple coordinate transformation from the location ofeither marker 291 and 292, or both.

Illumination of structures 293 and 294 by illumination beam 116 causesdiffraction of multiple orders across detector 119 in a vertical andhorizontal direction, respectively. The ratio of intensities between themeasured orders indicates the location of illumination beam 116 relativeto the boundary line shared by structures 293 and 294.

Similarly, as depicted in FIG. 19B periodic calibration target 295includes markers 296 and 297 readable by an optical microscope mountedto the specimen positioning system and two periodic zones locatedadjacent to one another along a boundary line. As depicted in FIG. 19B,the boundary line of target 295 is orthogonal to the boundary line oftarget 290. As depicted in FIG. 19B, a horizontally disposed periodicstructure 298 is located alongside a vertically disposed periodicstructure 299. Markers 296 and 297 are located in plane with theperiodic structures of the periodic calibration target. In addition, thelocation of markers 296 and 297 with respect to the boundary betweenstructures 298 and 299 is known precisely. In this manner, the locationof the boundary line is determined by simple coordinate transformationfrom the location of either marker 296 and 297, or both.

Illumination of structures 298 and 299 by illumination beam 116 causesdiffraction of multiple orders across detector 119 in a vertical andhorizontal direction, respectively. The ratio of intensities between themeasured orders indicates the location of illumination beam 116 relativeto the boundary line shared by structures 298 and 299.

In general, a periodic calibration target may include multiple differentperiodic zones in any suitable configuration. In some embodiments, theperiodic zones are arranged in a Cartesian pattern. However, otherpatterns of periodic zones may be contemplated.

FIG. 20 depicts a periodic calibration target 280 including markers 288and 289, and seven different periodic zones 281-287 arranged in ahexagonal pattern. Each periodic zone includes a different pitch, adifferent pitch orientation, or a combination thereof.

In another aspect, the shape of the surface of the wafer in theZ-direction is mapped using any of the alignment camera, an opticalproximity sensor, a capacitive proximity sensor, an interferometry basedsensor, or any other suitable proximity sensor. In some examples, thewafer surface is mapped on the front side (i.e., patterned side) of thewafer. In some other examples, the wafer surface is mapped on the backside (i.e., unpatterned side) of the wafer, provided the thickness ofthe wafer is sufficiently uniform, well modeled, or measured in-situ orapriori. In some embodiments, backside sensors are employed to measurewafer bow because many sensor technologies can be used to accuratelymeasure the location of unpatterned surface. In some of theseembodiments, backside sensors alone are employed to measure wafer bowacross the backside of the wafer and the wafer bow across the front sideis estimated based on a thickness model or a thickness mapping generatedfrom thickness measurements performed apriori. In some otherembodiments, backside and front side sensors are both employed tomeasure wafer bow. In some of these embodiments, backside sensors areemployed to measure wafer bow across the backside of the wafer and thewafer bow across the front side is estimated based on a thickness modelor a thickness mapping generated at least in part from estimates ofwafer thickness derived from front side and backside measurements. Insome examples, the wafer map is modeled using a number of standardinterpolators (e.g., polynomial basis functions, rational functions,neural networks, etc.). Furthermore, it is possible to couple thelateral displacements and the height displacements using an analyticalor numerical bending model of the wafer.

In a further aspect, the Z-actuators 150A-C are controlled to adjust theZ-position, Rx orientation, Ry orientation, or any combination thereof,in response to the shape of the surface of the wafer at the location ofincidence of illumination beam 116. In one example, the tilt of thewafer is corrected by Z-actuators 150A-C. The tilt correction may bebased on a map of wafer tilt or a value of tilt measured locally. Thiscan also be achieved using an optical based tilt sensor that monitorsthe Rx orientation and Ry orientation (i.e., tip and tilt) at the backsurface of the wafer.

In another further aspect, the Z-actuators 150A-C are controlled toadjust the Z-position, Rx orientation, Ry orientation, or anycombination thereof, to align the axis of rotation in azimuth with thestage reference frame 143. In one example, Z-actuators 150A-C areadjusted such that a specific target remains in focus of the alignmentcamera 154 over a range of azimuth angles. To perform this calibration,the wafer stage translates wafer 101 in the X and Y directions tomaintain the target in the field of view of the alignment camera 154 forall azimuth angles.

In general, it is not possible to calibrate for all offset effects.Calibration to remove the largest deviation is typically chosen andremaining offsets are either ignored or handled by stage maps thataccount for non-idealities in the wafer and stage.

In addition, changes in temperature and air pressure or any otherambient condition may have an effect on the positioning of theillumination beam. In some embodiments, beam motion is correlated tothese variables and the position of the beam is adjusted based onmeasured temperature and pressure and the correlation model.

In general, specimen positioning system 140 may include any suitablecombination of mechanical elements to achieve the desired linear andangular positioning performance, including, but not limited togoniometer stages, hexapod stages, angular stages, and linear stages.

In some embodiments, x-ray illumination source 110, focusing optics 111,slits 112 and 113, or any combination thereof, are maintained in thesame atmospheric environment as specimen 101 (e.g., gas purgeenvironment). However, in some embodiments, the optical path lengthbetween and within any of these elements is long and x-ray scattering inair contributes noise to the image on the detector. Hence in someembodiments, any of x-ray illumination source 110, focusing optics 111,and slits 112 and 113 are maintained in a localized, vacuum environment.In the embodiment depicted in FIG. 1, focusing optics 111, slits 112 and113, and beam shaping slit mechanism 120 are maintained in a controlledenvironment (e.g., vacuum) within an evacuated flight tube 118. Theillumination beam 116 passes through window 121 at the end of flighttube 118 before incidence with specimen 101.

In some embodiments, any of x-ray illumination source 110, focusingoptics 111, and slits 112 are and 113 are maintained in a localized,vacuum environment separated from one another and the specimen (e.g.,specimen 101) by vacuum windows. FIG. 21 is a diagram illustrative of avacuum chamber 160 containing x-ray illumination source 110, vacuumchamber 162 containing focusing optics 111, and vacuum chamber 163containing slits 112 and 113. The openings of each vacuum chamber arecovered by vacuum windows. For example, the opening of vacuum chamber160 is covered by vacuum window 161. Similarly, the opening of vacuumchamber 163 is covered by vacuum window 164. The vacuum windows may beconstructed of any suitable material that is substantially transparentto x-ray radiation (e.g., Kapton, Beryllium, etc.). A suitable vacuumenvironment is maintained within each vacuum chamber to minimizescattering of the illumination beam. A suitable vacuum environment mayinclude any suitable level of vacuum, any suitable purged environmentincluding a gas with a small atomic number (e.g., helium), or anycombination thereof. In this manner, as much of the illumination beampath as possible is located in vacuum to maximize flux and minimizescattering.

Similarly, in some embodiments, the optical path length between specimen101 and detector 119 (i.e., the collection beam path) is long and x-rayscattering in air contributes noise to the image on the detector. Hence,in preferred embodiments, a significant portion of the collection beampath length between specimen 101 and detector 119 is maintained in alocalized vacuum environment separated from the specimen (e.g., specimen101) by a vacuum window (e.g., vacuum window 124). In some embodiments,x-ray detector 119 is maintained in the same localized vacuumenvironment as the beam path length between specimen 101 and detector119. For example, as depicted in FIGS. 1 and 21, vacuum chamber 123maintains a localized vacuum environment surrounding detector 119 and asignificant portion of the beam path length between specimen 101 anddetector 119.

In some other embodiments, x-ray detector 119 is maintained in the sameatmospheric environment as specimen 101 (e.g., gas purge environment).This may be advantageous to remove heat from detector 119. However, inthese embodiments, it is preferable to maintain a significant portion ofthe beam path length between specimen 101 and detector 119 in alocalized vacuum environment within a vacuum chamber.

In some embodiments, the entire optical system, including specimen 101,is maintained in vacuum. However, in general, the costs associated withmaintaining specimen 101 in vacuum are high due to the complexitiesassociated with the construction of specimen positioning system 140.

In another further aspect, beam shaping slit mechanism 120 ismechanically integrated with vacuum chamber 163 to minimize the beampath length subject to the atmospheric environment. In general, it isdesirable to encapsulate as much of the beam as possible in vacuumbefore incidence with specimen 101. In some embodiments, the vacuum beamline extends into a hollow, cylindrically shaped cavity at the input ofbeam shaping slit mechanism 120. Vacuum window 164 is located at theoutput of vacuum chamber 163 within beam shaping slit mechanism 120 suchthat incoming beam 115 remains in vacuum within a portion of beamshaping slit mechanism 120, then passes through vacuum window 164 beforeinteraction with any of slits 126-129 and specimen 101.

In another further aspect, computing system 130 is configured togenerate a structural model (e.g., geometric model, material model, orcombined geometric and material model) of a measured structure of aspecimen, generate a T-SAXS response model that includes at least onegeometric parameter from the structural model, and resolve at least onespecimen parameter value by performing a fitting analysis of T-SAXSmeasurement data with the T-SAXS response model. The analysis engine isused to compare the simulated T-SAXS signals with measured data therebyallowing the determination of geometric as well as material propertiessuch as electron density of the sample. In the embodiment depicted inFIG. 1, computing system 130 is configured as a model building andanalysis engine configured to implement model building and analysisfunctionality as described herein.

FIG. 22 is a diagram illustrative of an exemplary model building andanalysis engine 180 implemented by computing system 130. As depicted inFIG. 22, model building and analysis engine 180 includes a structuralmodel building module 181 that generates a structural model 182 of ameasured structure of a specimen. In some embodiments, structural model182 also includes material properties of the specimen. The structuralmodel 182 is received as input to T-SAXS response function buildingmodule 183. T-SAXS response function building module 183 generates aT-SAXS response function model 184 based at least in part on thestructural model 182. In some examples, the T-SAXS response functionmodel 184 is based on x-ray form factors,

$\begin{matrix}{{F\left( \overset{\rho}{q} \right)} = {\int{{\rho\left( \overset{\rho}{r} \right)}e^{{- i}\;{\overset{\rho}{q} \cdot \overset{\rho}{r}}}d\overset{\rho}{r}}}} & (9)\end{matrix}$where F is the form factor, q is the scattering vector, and ρ(r) is theelectron density of the specimen in spherical coordinates. The x-rayscattering intensity is then given byI({right arrow over (q)})=F*F.  (10)T-SAXS response function model 184 is received as input to fittinganalysis module 185. The fitting analysis module 185 compares themodeled T-SAXS response with the corresponding measured data todetermine geometric as well as material properties of the specimen.

In some examples, the fitting of modeled data to experimental data isachieved by minimizing a chi-squared value. For example, for T-SAXSmeasurements, a chi-squared value can be defined as

$\begin{matrix}{\chi_{SAXS}^{2} = {\frac{1}{N_{SAXS}}{\sum\limits_{j}^{N_{SAXS}}\;\frac{\left( {{s_{j}^{{SAXS}\mspace{14mu}{model}}\left( {v_{1},\ldots\mspace{14mu},v_{L}} \right)} - s_{j}^{{SAXS}\mspace{14mu}{experiment}}} \right)^{2}}{\sigma_{{SAXS},j}^{2}}}}} & (11)\end{matrix}$

Where, S_(j) ^(SAXS experiment) is the measured T-SAXS signals 126 inthe “channel” j, where the index j describes a set of system parameterssuch as diffraction order, energy, angular coordinate, etc. S_(j)^(SAXS model)(v₁, . . . , v_(L)) is the modeled T-SAXS signal S_(j) forthe “channel” j, evaluated for a set of structure (target) parametersv₁, . . . , v_(L), where these parameters describe geometric (CD,sidewall angle, overlay, etc.) and material (electron density, etc.).σ_(SAXS,j) is the uncertainty associated with the jth channel. N_(SAXS)is the total number of channels in the x-ray metrology. L is the numberof parameters characterizing the metrology target.

Equation (11) assumes that the uncertainties associated with differentchannels are uncorrelated. In examples where the uncertaintiesassociated with the different channels are correlated, a covariancebetween the uncertainties, can be calculated. In these examples achi-squared value for T-SAXS measurements can be expressed as

$\begin{matrix}{\chi_{SAXS}^{2} = {\frac{1}{N_{SAXS}}\left( {{{\overset{\rightarrow}{S}}_{j}^{{SAXS}.\mspace{14mu}{model}}\left( {v_{1},\ldots\mspace{14mu},v_{M}} \right)} - {\overset{\rightarrow}{S}}_{j}^{{SAXS}.\mspace{14mu}{experiment}}} \right)^{T}{V_{SAXS}^{- 1}\left( {{{\overset{\rightarrow}{S}}_{j}^{{SAXS}.\mspace{14mu}{model}}\left( {v_{1},\ldots\mspace{14mu},v_{M}} \right)} - {\overset{\rightarrow}{S}}_{j}^{{SAXS}.\mspace{14mu}{experiment}}} \right)}}} & (12)\end{matrix}$

where, V_(SAXS) is the covariance matrix of the SAXS channeluncertainties, and T denotes the transpose.

In some examples, fitting analysis module 185 resolves at least onespecimen parameter value by performing a fitting analysis on T-SAXSmeasurement data 135 with the T-SAXS response model 184. In someexamples, χ_(SAXS) ² is optimized.

As described hereinbefore, the fitting of T-SAXS data is achieved byminimization of chi-squared values. However, in general, the fitting ofT-SAXS data may be achieved by other functions.

The fitting of T-SAXS metrology data is advantageous for any type ofT-SAXS technology that provides sensitivity to geometric and/or materialparameters of interest. Specimen parameters can be deterministic (e.g.,CD, SWA, etc.) or statistical (e.g., rms height of sidewall roughness,roughness correlation length, etc.) as long as proper models describingT-SAXS beam interaction with the specimen are used.

In general, computing system 130 is configured to access modelparameters in real-time, employing Real Time Critical Dimensioning(RTCD), or it may access libraries of pre-computed models fordetermining a value of at least one specimen parameter value associatedwith the specimen 101. In general, some form of CD-engine may be used toevaluate the difference between assigned CD parameters of a specimen andCD parameters associated with the measured specimen. Exemplary methodsand systems for computing specimen parameter values are described inU.S. Pat. No. 7,826,071, issued on Nov. 2, 2010, to KLA-Tencor Corp.,the entirety of which is incorporated herein by reference.

In some examples, model building and analysis engine 180 improves theaccuracy of measured parameters by any combination of feed sidewaysanalysis, feed forward analysis, and parallel analysis. Feed sidewaysanalysis refers to taking multiple data sets on different areas of thesame specimen and passing common parameters determined from the firstdataset onto the second dataset for analysis. Feed forward analysisrefers to taking data sets on different specimens and passing commonparameters forward to subsequent analyses using a stepwise copy exactparameter feed forward approach. Parallel analysis refers to theparallel or concurrent application of a non-linear fitting methodologyto multiple datasets where at least one common parameter is coupledduring the fitting.

Multiple tool and structure analysis refers to a feed forward, feedsideways, or parallel analysis based on regression, a look-up table(i.e., “library” matching), or another fitting procedure of multipledatasets. Exemplary methods and systems for multiple tool and structureanalysis is described in U.S. Pat. No. 7,478,019, issued on Jan. 13,2009, to KLA-Tencor Corp., the entirety of which is incorporated hereinby reference.

In another further aspect, an initial estimate of values of one or moreparameters of interest is determined based on T-SAXS measurementsperformed at a single orientation of the incident x-ray beam withrespect to the measurement target. The initial, estimated values areimplemented as the starting values of the parameters of interest for aregression of the measurement model with measurement data collected fromT-SAXS measurements at multiple orientations. In this manner, a closeestimate of a parameter of interest is determined with a relativelysmall amount of computational effort, and by implementing this closeestimate as the starting point for a regression over a much larger dataset, a refined estimate of the parameter of interest is obtained withless overall computational effort.

In another aspect, metrology tool 100 includes a computing system (e.g.,computing system 130) configured to implement beam control functionalityas described herein. In the embodiment depicted in FIG. 1, computingsystem 130 is configured as a beam controller operable to control any ofthe illumination properties such as intensity, divergence, spot size,polarization, spectrum, and positioning of the incident illuminationbeam 116.

As illustrated in FIG. 1, computing system 130 is communicativelycoupled to detector 119. Computing system 130 is configured to receivemeasurement data 135 from detector 119. In one example, measurement data135 includes an indication of the measured response of the specimen(i.e., intensities of the diffraction orders). Based on the distributionof the measured response on the surface of detector 119, the locationand area of incidence of illumination beam 116 on specimen 101 isdetermined by computing system 130. In one example, pattern recognitiontechniques are applied by computing system 130 to determine the locationand area of incidence of illumination beam 116 on specimen 101 based onmeasurement data 135. In some examples, computing system 130communicates command signals 137 to x-ray illumination source 110 toselect the desired illumination wavelength. In some examples, computingsystem 130 communicates command signals 138 to actuator subsystem 111′to redirect the x-ray emission relative to base frame 141 to achieve adesired beam direction. In some examples, computing system 130communicates command signals 136 to beam shaping slit mechanism 120 tochange the beam spot size such that incident illumination beam 116arrives at specimen 101 with the desired beam spot size and orientation.In one example, command signals 136 cause rotary actuator 122, depictedin FIG. 5, to rotate beam shaping slit mechanism 120 to a desiredorientation with respect to specimen 101. In another example, commandsignals 136 cause actuators associated with each of slits 126-129 tochange position to reshape the incident beam 116 to a desired shape andsize. In some other examples, computing system 130 communicates acommand signal to wafer positioning system 140 to position and orientspecimen 101 such that incident illumination beam 116 arrives at thedesired location and angular orientation with respect to specimen 101.

In a further aspect, T-SAXS measurement data is used to generate animage of a measured structure based on the measured intensities of thedetected diffraction orders. In some embodiments, a T-SAXS responsefunction model is generalized to describe the scattering from a genericelectron density mesh. Matching this model to the measured signals,while constraining the modelled electron densities in this mesh toenforce continuity and sparse edges, provides a three dimensional imageof the sample.

Although, geometric, model-based, parametric inversion is preferred forcritical dimension (CD) metrology based on T-SAXS measurements, a map ofthe specimen generated from the same T-SAXS measurement data is usefulto identify and correct model errors when the measured specimen deviatesfrom the assumptions of the geometric model.

In some examples, the image is compared to structural characteristicsestimated by a geometric, model-based parametric inversion of the samescatterometry measurement data. Discrepancies are used to update thegeometric model of the measured structure and improve measurementperformance. The ability to converge on an accurate parametricmeasurement model is particularly important when measuring integratedcircuits to control, monitor, and trouble-shoot their manufacturingprocess.

In some examples, the image is a two dimensional (2-D) map of electrondensity, absorptivity, complex index of refraction, or a combination ofthese material characteristics. In some examples, the image is a threedimensional (3-D) map of electron density, absorptivity, complex indexof refraction, or a combination of these material characteristics. Themap is generated using relatively few physical constraints. In someexamples, one or more parameters of interest, such as critical dimension(CD), sidewall angle (SWA), overlay, edge placement error, pitch walk,etc., are estimated directly from the resulting map. In some otherexamples, the map is useful for debugging the wafer process when thesample geometry or materials deviate outside the range of expectedvalues contemplated by a parametric structural model employed formodel-based CD measurement. In one example, the differences between themap and a rendering of the structure predicted by the parametricstructural model according to its measured parameters are used to updatethe parametric structural model and improve its measurement performance.Further details are described in U.S. Patent Publication No.2015/0300965, the content of which is incorporated herein by referenceit its entirety. Additional details are described in U.S. PatentPublication No. 2015/0117610, the content of which is incorporatedherein by reference it its entirety.

In a further aspect, model building and analysis engine 180 is employedto generate models for combined x-ray and optical measurement analysis.In some examples, optical simulations are based on, e.g., rigorouscoupled-wave analysis (RCWA) where Maxwell's equations are solved tocalculate optical signals such as reflectivities for differentpolarizations, ellipsometric parameters, phase change, etc.

Values of one or more parameters of interest are determined based on acombined fitting analysis of the detected intensities of the x-raydiffraction orders at the plurality of different angles of incidence anddetected optical intensities with a combined, geometricallyparameterized response model. The optical intensities are measured by anoptical metrology tool that may or may not be mechanically integratedwith an x-ray metrology system, such as systems 100 depicted in FIG. 1.Further details are described in U.S. Patent Publication No.2014/0019097 and U.S. Patent Publication No. 2013/0304424, the contentsof each are incorporated herein by reference it their entirety.

In general, a metrology target is characterized by an aspect ratiodefined as a maximum height dimension (i.e., dimension normal to thewafer surface) divided by a maximum lateral extent dimension (i.e.,dimension aligned with the wafer surface) of the metrology target. Insome embodiments, the metrology target under measurement has an aspectratio of at least twenty. In some embodiments, the metrology target hasan aspect ratio of at least forty.

It should be recognized that the various steps described throughout thepresent disclosure may be carried out by a single computer system 130or, alternatively, a multiple computer system 130. Moreover, differentsubsystems of the system 100, such as the specimen positioning system140, may include a computer system suitable for carrying out at least aportion of the steps described herein. Therefore, the aforementioneddescription should not be interpreted as a limitation on the presentinvention but merely an illustration. Further, the one or more computingsystems 130 may be configured to perform any other step(s) of any of themethod embodiments described herein.

In addition, the computer system 130 may be communicatively coupled tothe x-ray illumination source 110, beam shaping slit mechanism 120,specimen positioning system 140, and detector 119 in any manner known inthe art. For example, the one or more computing systems 130 may becoupled to computing systems associated with the x-ray illuminationsource 110, beam shaping slit mechanism 120, specimen positioning system140, and detector 119, respectively. In another example, any of thex-ray illumination source 110, beam shaping slit mechanism 120, specimenpositioning system 140, and detector 119 may be controlled directly by asingle computer system coupled to computer system 130.

The computer system 130 may be configured to receive and/or acquire dataor information from the subsystems of the system (e.g., x-rayillumination source 110, beam shaping slit mechanism 120, specimenpositioning system 140, detector 119, and the like) by a transmissionmedium that may include wireline and/or wireless portions. In thismanner, the transmission medium may serve as a data link between thecomputer system 130 and other subsystems of the system 100.

Computer system 130 of the metrology system 100 may be configured toreceive and/or acquire data or information (e.g., measurement results,modeling inputs, modeling results, etc.) from other systems by atransmission medium that may include wireline and/or wireless portions.In this manner, the transmission medium may serve as a data link betweenthe computer system 130 and other systems (e.g., memory on-boardmetrology system 100, external memory, or external systems). Forexample, the computing system 130 may be configured to receivemeasurement data (e.g., signals 135) from a storage medium (i.e., memory132 or 190) via a data link. For instance, spectral results obtainedusing detector 119 may be stored in a permanent or semi-permanent memorydevice (e.g., memory 132 or 190). In this regard, the measurementresults may be imported from on-board memory or from an external memorysystem. Moreover, the computer system 130 may send data to other systemsvia a transmission medium. For instance, specimen parameter values 186determined by computer system 130 may be stored in a permanent orsemi-permanent memory device (e.g., memory 190). In this regard,measurement results may be exported to another system.

Computing system 130 may include, but is not limited to, a personalcomputer system, mainframe computer system, workstation, image computer,parallel processor, or any other device known in the art. In general,the term “computing system” may be broadly defined to encompass anydevice having one or more processors, which execute instructions from amemory medium.

Program instructions 134 implementing methods such as those describedherein may be transmitted over a transmission medium such as a wire,cable, or wireless transmission link. For example, as illustrated inFIG. 1, program instructions stored in memory 132 are transmitted toprocessor 131 over bus 133. Program instructions 134 are stored in acomputer readable medium (e.g., memory 132). Exemplary computer-readablemedia include read-only memory, a random access memory, a magnetic oroptical disk, or a magnetic tape.

FIG. 23 illustrates a method 300 suitable for implementation by themetrology system 100 of the present invention. In one aspect, it isrecognized that data processing blocks of method 300 may be carried outvia a pre-programmed algorithm executed by one or more processors ofcomputing system 130. While the following description is presented inthe context of metrology system 100, it is recognized herein that theparticular structural aspects of metrology system 100 do not representlimitations and should be interpreted as illustrative only.

In block 301, an x-ray illumination beam is generated by an x-rayillumination subsystem.

In block 302, a specimen is positioned with respect to the x-rayillumination beam such that the x-ray illumination beam is incident onthe surface of the specimen at any location on the surface of thespecimen.

In block 303, the specimen is rotated with respect to the x-rayillumination beam about an axis of rotation such that the x-rayillumination beam is incident on the surface of the specimen at anylocation at a plurality of angles of incidence.

In block 304, the specimen is rotated about an azimuth axis of rotationsuch that the x-ray illumination beam is incident on the surface of thespecimen at any location at a plurality of azimuth angles.

In block 305, a calibration target is illuminated with the x-rayillumination beam. The calibration target includes one or more markers.

In block 306, an amount of transmitted flux is detected over a range ofpositions of the specimen positioning system, wherein at least a portionof the x-ray illumination beam is incident on the calibration targetover the range of positions.

In block 307, a location of incidence of the x-ray illumination beam isdetermined with respect the specimen positioning system based on thedetected amount of transmitted flux.

In some embodiments, scatterometry measurements as described herein areimplemented as part of a fabrication process tool. Examples offabrication process tools include, but are not limited to, lithographicexposure tools, film deposition tools, implant tools, and etch tools. Inthis manner, the results of a T-SAXS analysis are used to control afabrication process. In one example, T-SAXS measurement data collectedfrom one or more targets is sent to a fabrication process tool. TheT-SAXS measurement data is analyzed as described herein and the resultsused to adjust the operation of the fabrication process tool.

Scatterometry measurements as described herein may be used to determinecharacteristics of a variety of semiconductor structures. Exemplarystructures include, but are not limited to, FinFETs, low-dimensionalstructures such as nanowires or graphene, sub 10 nm structures,lithographic structures, through substrate vias (TSVs), memorystructures such as DRAM, DRAM 4F2, FLASH, MRAM and high aspect ratiomemory structures. Exemplary structural characteristics include, but arenot limited to, geometric parameters such as line edge roughness, linewidth roughness, pore size, pore density, side wall angle, profile,critical dimension, pitch, thickness, overlay, and material parameterssuch as electron density, composition, grain structure, morphology,stress, strain, and elemental identification. In some embodiments, themetrology target is a periodic structure. In some other embodiments, themetrology target is aperiodic.

In some examples, measurements of critical dimensions, thicknesses,overlay, and material properties of high aspect ratio semiconductorstructures including, but not limited to, spin transfer torque randomaccess memory (STT-RAM), three dimensional NAND memory (3D-NAND) orvertical NAND memory (V-NAND), dynamic random access memory (DRAM),three dimensional FLASH memory (3D-FLASH), resistive random accessmemory (Re-RAM), and phase change random access memory (PC-RAM) areperformed with T-SAXS measurement systems as described herein.

As described herein, the term “critical dimension” includes any criticaldimension of a structure (e.g., bottom critical dimension, middlecritical dimension, top critical dimension, sidewall angle, gratingheight, etc.), a critical dimension between any two or more structures(e.g., distance between two structures), and a displacement between twoor more structures (e.g., overlay displacement between overlayinggrating structures, etc.). Structures may include three dimensionalstructures, patterned structures, overlay structures, etc.

As described herein, the term “critical dimension application” or“critical dimension measurement application” includes any criticaldimension measurement.

As described herein, the term “metrology system” includes any systememployed at least in part to characterize a specimen in any aspect,including critical dimension applications and overlay metrologyapplications. However, such terms of art do not limit the scope of theterm “metrology system” as described herein. In addition, the metrologysystems described herein may be configured for measurement of patternedwafers and/or unpatterned wafers. The metrology system may be configuredas a LED inspection tool, edge inspection tool, backside inspectiontool, macro-inspection tool, or multi-mode inspection tool (involvingdata from one or more platforms simultaneously), and any other metrologyor inspection tool that benefits from the measurement techniquesdescribed herein.

Various embodiments are described herein for a semiconductor processingsystem (e.g., an inspection system or a lithography system) that may beused for processing a specimen. The term “specimen” is used herein torefer to a wafer, a reticle, or any other sample that may be processed(e.g., printed or inspected for defects) by means known in the art.

As used herein, the term “wafer” generally refers to substrates formedof a semiconductor or non-semiconductor material. Examples include, butare not limited to, monocrystalline silicon, gallium arsenide, andindium phosphide. Such substrates may be commonly found and/or processedin semiconductor fabrication facilities. In some cases, a wafer mayinclude only the substrate (i.e., bare wafer). Alternatively, a wafermay include one or more layers of different materials formed upon asubstrate. One or more layers formed on a wafer may be “patterned” or“unpatterned.” For example, a wafer may include a plurality of dieshaving repeatable pattern features.

A “reticle” may be a reticle at any stage of a reticle fabricationprocess, or a completed reticle that may or may not be released for usein a semiconductor fabrication facility. A reticle, or a “mask,” isgenerally defined as a substantially transparent substrate havingsubstantially opaque regions formed thereon and configured in a pattern.The substrate may include, for example, a glass material such asamorphous SiO₂. A reticle may be disposed above a resist-covered waferduring an exposure step of a lithography process such that the patternon the reticle may be transferred to the resist.

One or more layers formed on a wafer may be patterned or unpatterned.For example, a wafer may include a plurality of dies, each havingrepeatable pattern features. Formation and processing of such layers ofmaterial may ultimately result in completed devices. Many differenttypes of devices may be formed on a wafer, and the term wafer as usedherein is intended to encompass a wafer on which any type of deviceknown in the art is being fabricated.

In one or more exemplary embodiments, the functions described may beimplemented in hardware, software, firmware, or any combination thereof.If implemented in software, the functions may be stored on ortransmitted over as one or more instructions or code on acomputer-readable medium. Computer-readable media includes both computerstorage media and communication media including any medium thatfacilitates transfer of a computer program from one place to another. Astorage media may be any available media that can be accessed by ageneral purpose or special purpose computer. By way of example, and notlimitation, such computer-readable media can comprise RAM, ROM, EEPROM,CD-ROM or other optical disk storage, magnetic disk storage or othermagnetic storage devices, or any other medium that can be used to carryor store desired program code means in the form of instructions or datastructures and that can be accessed by a general-purpose orspecial-purpose computer, or a general-purpose or special-purposeprocessor. Also, any connection is properly termed a computer-readablemedium. For example, if the software is transmitted from a website,server, or other remote source using a coaxial cable, fiber optic cable,twisted pair, digital subscriber line (DSL), or wireless technologiessuch as infrared, radio, and microwave, then the coaxial cable, fiberoptic cable, twisted pair, DSL, or wireless technologies such asinfrared, radio, and microwave are included in the definition of medium.Disk and disc, as used herein, includes compact disc (CD), laser disc,XRF disc, digital versatile disc (DVD), floppy disk and blu-ray discwhere disks usually reproduce data magnetically, while discs reproducedata optically with lasers. Combinations of the above should also beincluded within the scope of computer-readable media.

Although certain specific embodiments are described above forinstructional purposes, the teachings of this patent document havegeneral applicability and are not limited to the specific embodimentsdescribed above. Accordingly, various modifications, adaptations, andcombinations of various features of the described embodiments can bepracticed without departing from the scope of the invention as set forthin the claims.

What is claimed is:
 1. A metrology system comprising: an x-rayillumination source configured to generate an x-ray illumination beamincident on a semiconductor wafer; a specimen positioning systemconfigured to actively control a position of the semiconductor wafer insix degrees of freedom with respect to the x-ray illumination beam,wherein a vector normal to a surface of the wafer is approximatelyperpendicular to a direction of a gravitational force imposed on thesemiconductor wafer by gravity during measurement of the semiconductorwafer by the metrology system; an x-ray detector configured to detect afirst amount of x-ray radiation from the semiconductor wafer in responseto the incident x-ray illumination beam; and a computing systemconfigured to determine a value of a parameter of interestcharacterizing a structure disposed on the semiconductor wafer.
 2. Themetrology system of claim 1, the specimen positioning system comprising:a base frame; a stage reference frame configured to rotate with respectto the base frame about an axis of rotation that is perpendicular to theillumination beam and approximately parallel to the wafer surface; awafer stage mounted to stage reference frame, the wafer stage configuredto locate the wafer with respect to the incident illumination beam atany desired location over an active area of the semiconductor wafer; athree axis stage mounted to the wafer stage configured to move thesemiconductor wafer in a direction approximately aligned with theillumination beam and to rotate the semiconductor wafer about twoorthogonal axes of rotation, both approximately perpendicular to theillumination beam; and a rotary stage mounted to the three axis stage,the rotary stage configured to rotate the wafer about an axisapproximately normal to the wafer surface.
 3. The metrology system ofclaim 2, wherein the wafer stage and the three axis stage aremechanically coupled by six points of mechanical contact arranged in akinematic coupling.
 4. The metrology system of claim 1, the specimenpositioning system comprising one or more sensors configured to measurea location of a back-side surface of the semiconductor wafer withrespect to the specimen positioning system in a direction approximatelynormal to the wafer surface, one or more sensors configured to measure alocation of a front-side surface of the semiconductor wafer with respectto the specimen positioning system in a direction approximately normalto the wafer surface, or a combination thereof.
 5. The metrology systemof claim 2, the specimen positioning system comprising one or more edgegripper devices configured to mechanically couple the semiconductorwafer to the rotary stage at the edges of the semiconductor wafer. 6.The metrology system of claim 1, the specimen positioning systemcomprising a rotary counterweight disposed on the stage reference frame,wherein a center of mass of the stage reference frame configured torotate with respect to the base frame about the axis of rotation isapproximately aligned with the axis of rotation.
 7. The metrology systemof claim 1, further comprising: a first vacuum chamber enveloping asignificant portion of an illumination beam path between the x-rayillumination source and the semiconductor wafer.
 8. The metrology systemof claim 1, further comprising: a first vacuum chamber enveloping asignificant portion of a collection beam path between the semiconductorwafer and the x-ray detector.
 9. A metrology system comprising: an x-rayillumination subsystem configured to generate an x-ray illuminationbeam; a specimen positioning system configured to position a specimenwith respect to the x-ray illumination beam such that the x-rayillumination beam is incident on the surface of the specimen at anylocation on the surface of the specimen and rotate the specimen withrespect to the x-ray illumination beam about an axis of rotation suchthat the x-ray illumination beam is incident on the surface of thespecimen at any location at a plurality of angles of incidence androtate the specimen about an azimuth axis of rotation such that thex-ray illumination beam is incident on the surface of the specimen atany location at a plurality of azimuth angles; a beam occlusioncalibration target including a cylindrical pin and one or more markersdisposed in a plane aligned with a central axis of the cylindrical pin;an x-ray detector configured to detect an amount of transmitted fluxover a range of positions of the specimen positioning system, wherein atleast a portion of the x-ray illumination beam is incident on thecylindrical pin over the range of positions; and a computing systemconfigured to determine a location of incidence of the x-rayillumination beam with respect the specimen positioning system based onthe detected amount of transmitted flux.
 10. The metrology system ofclaim 9, wherein the range of positions includes a range of angles ofincidence, and wherein the computing system is further configured todetermine an adjustment of a position of the axis of rotation withrespect to the x-ray illumination beam to align the axis of rotation andthe x-ray illumination beam.
 11. The metrology system of claim 10,wherein the determining of the adjustment of the position of the axis ofrotation with respect to the x-ray illumination beam is based on thedetected amount of transmitted flux.
 12. The metrology system of claim10, further comprising: an alignment camera that generates a pluralityof images of at least a portion of the one or more markers or one ormore markers disposed on the specimen at a plurality of different anglesof incidence, and wherein a misalignment of the position of the axis ofrotation with respect to the one or more markers or the one or moremarkers disposed on the specimen is determined based on a displacementof the one or more markers or the one or more markers disposed on thespecimen measured in the plurality of images.
 13. The metrology systemof claim 10, further comprising: one or more actuators configured toadjust a position of one or more elements of the x-ray illuminationsubsystem to adjust the position of the axis of rotation with respect tothe x-ray illumination beam.
 14. The metrology system of claim 10,further comprising: one or more actuators configured to adjust theposition of specimen positioning system with respect to the x-rayillumination beam to align the axis of rotation and the x-rayillumination beam.
 15. The metrology system of claim 9, wherein thedetermining of the location of incidence of the x-ray illumination beamwith respect the specimen positioning system is based on a model oftransmitted flux as a function of position of the cylindrical pin withrespect to the x-ray illumination beam.
 16. The metrology system ofclaim 9, further comprising: an alignment camera that generates an imageof at least a portion of the marker, wherein the computing system isfurther configured to locate the marker in the coordinate system of thespecimen positioning system based on the image and estimate a locationof incidence of the x-ray illumination beam in the coordinate system ofthe specimen positioning system based on the location of the marker anda known distance between the marker and the cylindrical pin.
 17. Themetrology system of claim 16, wherein the alignment camera generates animage of at least one fiducial marker disposed on the specimen, andwherein the computing system is further configured to locate thefiducial marker in the coordinate system of the specimen positioningsystem based on the image.
 18. The metrology system of claim 17, whereinthe alignment camera rotates about the axis of rotation with thespecimen.
 19. The metrology system of claim 9, further comprising: oneor more sensors configured to measure a location of a back-side surfaceof the specimen with respect to the specimen positioning system in adirection approximately normal to the wafer surface, one or more sensorsconfigured to measure a location of a front-side surface of the specimenwith respect to the specimen positioning system in a directionapproximately normal to the wafer surface, or a combination thereof. 20.The metrology system of claim 9, wherein the beam occlusion calibrationtarget is disposed on the specimen positioning system or the specimen.21. The metrology system of claim 9, further comprising: a first vacuumchamber enveloping a significant portion of an illumination beam pathbetween the x-ray illumination source and the specimen.
 22. Themetrology system of claim 9, further comprising: a first vacuum chamberenveloping a significant portion of a collection beam path between thespecimen and the x-ray detector.
 23. A metrology system comprising: anx-ray illumination source configured to generate an x-ray illuminationbeam; a specimen positioning system configured to position a specimenwith respect to the x-ray illumination beam such that the x-rayillumination beam is incident on the surface of the specimen at anylocation on the surface of the specimen and rotate the specimen withrespect to the x-ray illumination beam about an axis of rotation suchthat the x-ray illumination beam is incident on the surface of thespecimen at any location at a plurality of angles of incidence androtate the specimen about an azimuth axis of rotation such that thex-ray illumination beam is incident on the surface of the specimen atany location at a plurality of azimuth angles, wherein each of theplurality of angles of incidence describes an angle between the x-rayillumination beam and the surface of the specimen; a periodiccalibration target including one or more periodic structures of knownextent on the periodic calibration target and one or more markersdisposed in a plane aligned with the one or more periodic structures; anx-ray detector configured to detect an amount of transmitted flux over arange of positions of the specimen positioning system, wherein at leasta portion of the x-ray illumination beam is incident on the one or moreperiodic structures over the range of positions; and a computing systemconfigured to determine a location of incidence of the x-rayillumination beam with respect the specimen positioning system based onthe detected amount of transmitted flux.
 24. The metrology system ofclaim 23, wherein the range of positions includes a range of angles ofincidence, and wherein the computing system is further configured todetermine an adjustment of a position of the axis of rotation withrespect to the x-ray illumination beam based on the detected amount oftransmitted flux.
 25. The metrology system of claim 23, wherein theperiodic calibration target includes a boundary line between twoperiodic structures that differ in periodicity, orientation, or both.26. The metrology system of claim 23, wherein the periodic calibrationtarget includes an intersection point among three of more periodicstructures that differ in periodicity, orientation, or both.
 27. Themetrology system of claim 23, wherein the periodic calibration target isdisposed on the specimen positioning system or the specimen.
 28. Amethod comprising: generating an x-ray illumination beam by an x-rayillumination subsystem; positioning a specimen with respect to the x-rayillumination beam such that the x-ray illumination beam is incident onthe surface of the specimen at any location on the surface of thespecimen; rotating the specimen with respect to the x-ray illuminationbeam about an axis of rotation such that the x-ray illumination beam isincident on the surface of the specimen at any location at a pluralityof angles of incidence, wherein each of the plurality of angles ofincidence describes an angle between the x-ray illumination beam and thesurface of the specimen; rotating the specimen about an azimuth axis ofrotation such that the x-ray illumination beam is incident on thesurface of the specimen at any location at a plurality of azimuthangles; illuminating a calibration target with the x-ray illuminationbeam, the calibration target including one or more markers; detecting anamount of transmitted flux over a range of positions of the specimenpositioning system, wherein at least a portion of the x-ray illuminationbeam is incident on the calibration target over the range of positions;and determining a location of incidence of the x-ray illumination beamwith respect the specimen positioning system based on the detectedamount of transmitted flux.
 29. The method of claim 28, furthercomprising: determining an adjustment of a position of the axis ofrotation with respect to the x-ray illumination beam to align the axisof rotation and the x-ray illumination beam, wherein the range ofpositions includes a range of angles of incidence.
 30. The method ofclaim 29, wherein the determining of the adjustment of the position ofthe axis of rotation with respect to the x-ray illumination beam isbased on the detected amount of transmitted flux.
 31. The method ofclaim 29, further comprising: generating a plurality of images of atleast a portion of the one or more markers or one or more markersdisposed on the specimen at a plurality of different angles ofincidence, wherein a misalignment of the position of the axis ofrotation with respect to the one or more markers or the one or moremarkers disposed on the specimen is determined based on a displacementof the one or more markers or the one or more markers disposed on thespecimen measured in the plurality of images.
 32. The method of claim29, further comprising: adjusting a position of one or more elements ofthe x-ray illumination subsystem to adjust the position of the axis ofrotation with respect to the x-ray illumination beam.
 33. The method ofclaim 29, further comprising: adjusting the position of specimenpositioning system with respect to the x-ray illumination beam to alignthe axis of rotation and the x-ray illumination beam.
 34. The method ofclaim 28, wherein the calibration target includes one or more periodicstructures of known extent, and wherein the one or more markers aredisposed in a plane aligned with the one or more periodic structures.35. The method of claim 28, wherein the calibration target includes acylindrical pin, wherein the one or more markers are disposed in a planealigned with a central axis of the cylindrical pin.